Information transmission apparatus, information transmission method, information reception apparatus, and information reception method

ABSTRACT

A high-performance decoding process allowing the degree of design freedom to be increased substantially has been implemented. A transmission apparatus ( 10 ) of a data transmission and reception system comprises converters ( 11   0 ), ( 11   1 ) and ( 11   2 ), multipliers ( 12   0 ), ( 12   1 ) and ( 12   2 ), adders ( 13   0 ) and ( 13   1 ) and a transmission unit  14.  The converters ( 11   0 ), ( 11   1 ) and ( 11   2 ) convert information-bit sequences b (0) , b (1)  and b (2)  respectively into encoded sequences x (0) , x (1)  and x (2)  respectively. The multipliers ( 12   0 ), ( 12   1 ) and ( 12   2 ) multiply respectively the encoded sequences x (0) , x (1)  and x (2)  by constants a (0) , a (1)  and a (2)  respectively. The adder ( 13   0 ) adds a constant-times encoded sequence a (0) x (0)  produced by the multiplier ( 12   0 ) as a result of multiplication to a constant-times encoded sequence a (1) x (1)  produced by the multiplier ( 12   1 ) as a result of multiplication. The adder ( 13   1 ) adds an additive encoded sequence a (0) x (0) +a (1) x (1)  produced by the adder ( 13   0 ) as a result of addition to a constant-times encoded sequence a (2) x (2)  produced by the multiplier ( 12   2 ) as a result of multiplication. The transmission unit  14  transmits an additive encoded sequence g(=a (0) x (0) +a (1) x (1) +a (2) x (2) ) produced by the adder ( 13   1 ) as a result of addition to an external apparatus as a transmitted signal g′.

TECHNICAL FIELD

[0001] The present invention relates to an information transmissionapparatus and an information transmission method, which are used forconverting the format of information into a predetermined format and fortransmitting the information with the predetermined format, as well asrelates to an information reception apparatus and an informationreception method, which are used for receiving a signal comprising asequence of codes and a predetermined noise added to the sequence ofcodes, from the information transmission apparatus.

BACKGROUND ART

[0002] In recent years, research is conducted extensively andintensively in communication fields such as mobile communications anddeep space communications as well as broadcasting fields such asground-wave broadcasting and satellite digital broadcasting. Along withsuch research, there is also performed other research in a coding theoryfor the purpose of increasing the efficiencies of error-correctionencoding and decoding processes.

[0003] As a theoretical limit of a communication-line encodingperformance, there is known C. E. Shannon's limit given by so-calledShannon's communication line coding theorem.

[0004] The research in the coding theory is carried out for the purposeof developing a code exhibiting performance close to Shannon's limit. Inrecent years, as codes produced by encoding methods to exhibitperformance close to Shannon's limit, for example, there have beendeveloped the so-called Parallel Concatenated Convolutional Codes andthe so-called Serial Concatenated Convolutional Codes, which arereferred to hereafter simply as the PCCC and the SCCC respectively.

[0005] In recent years, on the other hand, there is also conductedresearch in methods of decoding these codes. To put it concretely, thereis conducted research to decrease a symbol error rate by carrying out asoft-output operation on a decoded output of an internal code inconcatenated codes and an output of each repetitive decoding operationadopting a repetitive decoding method. In addition, there is alsoextensively conducted research on decoding methods suitable for suchcodes. As a method to minimize a symbol error rate in a process todecode a predetermined code such as convolutional codes, for example,there are known a technique based on a BCJR algorithm and a techniquebased on a max-log-MAP algorithm and a log-MAP algorithm, which are eachan improved BCR algorithm. The BCR algorithm is described by Bahl,Cocke, Jelinek and Raviv in a reference with a title of “Optimaldecoding of Linear Codes for Minimizing Symbol Error Rate,” IEEE Trans.Inf. Theory, vol. IT-20, pp. 284-287, March 1974. On the other hand, themax-log-MAP algorithm and the log-MAP algorithm are described byRobertson, Villebrun and Hoeher in a reference with a title of “AComparison of Optimal and Sub-Optimal MAP Decoding Algorithms Operatingin the Domain,” IEEE Int. Conf. on Communications, pp. 1009-1013, June1995. The max-log-MAP algorithm and the log-MAP algorithm are referredto hereafter as a max-log-BCJR algorithm and a log-BCJR algorithmrespectively. The PCCC and the SCCC described above are decoded bycarrying out the so-called repetitive decoding operation among aplurality of decoders, which carry out a MAP (Maximum A Posteriori)probability decoding process based on the BCR algorithm, themax-log-BCJR algorithm and the log-BCJR algorithm.

[0006] By the way, an encoding process is followed by signal-pointmapping for bit data obtained as a result of the encoding process. Thesignal-point mapping is based on a multi-value modulation techniquedetermined in advance. Examples of the multi-value modulation techniqueare an 8-PSK (Phase Shift Keying) modulation technique, a 16-QAM(Quadrature Amplitude Modulation) technique and a 64-QAM (QuadratureAmplitude Modulation) technique.

[0007] If an encoding process is followed by signal-point mapping basedon the multi-value modulation technique determined in advance, however,it is impossible to make a margin for a noise of the encoded datacompletely match a margin for a noise found by the mapping. As a result,the transmission characteristics including a bit error rate deteriorate.

[0008] It is thus an object of the present invention addressing theproblem described above to provide an information transmission apparatusand an information transmission method that are capable of implementinga high-performance encoding process with ease as a result of newlydeveloping an encoding technique considered to be theoretically optimumfor an encoding process adopting typically the multi-value modulationtechnique.

[0009] In addition, it is another object of the present invention toprovide an information reception apparatus and an information receptionmethod that are capable of easily decoding data obtained as a resultproduced by the information transmission apparatus and the informationtransmission method with a high degree of precision.

DISCLOSURE OF INVENTION

[0010] In order to achieve the objects described above, in accordancewith an aspect of the present invention, there is provided aninformation transmission apparatus, which is used for converting theformat of input information into a predetermined format prior totransmission of the information, characterized in that the informationtransmission apparatus includes: a first conversion means for convertinga first information-bit sequence comprising a predetermined number ofbits into a first encoded sequence comprising M numbers; a firstmultiplication means for multiplying the first encoded sequence producedby the first conversion means as a result of a conversion process by afirst constant; at least a second conversion means for converting asecond information-bit sequence comprising a predetermined number ofbits into a second encoded sequence comprising M numbers; at least asecond multiplication means for multiplying the second encoded sequenceproduced by the second conversion means as a result of a conversionprocess by a second constant; an addition means for adding theconstituent of a first constant-times encoded sequence produced by thefirst multiplication means as a result of a multiplication process tothe constituent of a second constant-times encoded sequence produced bythe second multiplication means as a result of a multiplication processto produce an additive encoded sequence; and a transmission means fortransmitting the additive encoded sequence as a transmitted signal.

[0011] As described above, in the information transmission apparatusprovided by the present invention, the addition means adds a firstconstant-times encoded sequence produced by the first multiplicationmeans as a product of a first encoded sequence and a first constant to asecond constant-times encoded sequence produced by the secondmultiplication means as a product of a second encoded sequence and asecond constant to produce an additive encoded sequence, and thetransmission means transmits the additive encoded sequence.

[0012] In addition, in accordance with the present invention whichachieves above-described object, there is provided an informationtransmission method, which is used for converting the format of inputinformation into a predetermined format prior to transmission of theinformation, including: a first conversion process of converting a firstinformation-bit sequence comprising a predetermined number of bits intoa first encoded sequence comprising M numbers; a first multiplicationprocess of multiplying the first encoded sequence produced by the firstconversion process as a result of conversion by a first constant; atleast a second conversion process of converting a second information-bitsequence comprising a predetermined number of bits into a second encodedsequence comprising M numbers; at least a second multiplication processof multiplying the second encoded sequence produced by the secondconversion process as a result of conversion by a second constant; anaddition process of adding the constituent of a first constant-timesencoded sequence produced by the first multiplication process as aresult of multiplication to the constituent of a second constant-timesencoded sequence produced by the second multiplication process as aresult of multiplication to produce an additive encoded sequence; and atransmission process of transmitting the additive encoded sequence as atransmitted signal.

[0013] As described above, in the addition process of the informationtransmission method provided by the present invention, a firstconstant-times encoded sequence produced by the first multiplicationprocess as a product of a first encoded sequence and a first constant isadded to a second constant-times encoded sequence produced by the secondmultiplication process as a product of a second encoded sequence and asecond constant to produce an additive encoded sequence, and in thetransmission process of the information transmission method, theadditive encoded sequence is transmitted.

[0014] In addition, in accordance with the present invention thatachieves above-described object, there is provided an informationreception apparatus for receiving a reception signal comprising anadditive encoded sequence and a predetermined noise added to theadditive encoded sequence transmitted by an information transmissionapparatus including: a first conversion means for converting a firstinformation-bit sequence comprising a predetermined number of bits intoa first encoded sequence comprising M numbers; a first multiplicationmeans for multiplying the first encoded sequence produced by the firstconversion means as a result of conversion by a first constant; at leasta second conversion means for converting a second information-bitsequence comprising a predetermined number of bits into a second encodedsequence comprising M numbers; at least a second multiplication meansfor multiplying the second encoded sequence produced by the secondconversion means as a result of conversion by a second constant; anaddition means for adding the constituent of a first constant-timesencoded sequence produced by the first multiplication means as a resultof multiplication to the constituent of a second constant-times encodedsequence produced by the second multiplication means as a result ofmultiplication to produce the additive encoded sequence; and atransmission means for transmitting the additive encoded sequence as thetransmitted signal, wherein the information reception apparatus ischaracterized in that the information reception apparatus includes: areception means for receiving the reception signal; and a decoding meansfor carrying out a decoding process to produce at least one of the firstinformation-bit sequence and the second information-bit sequence on thebasis of a received value received from the reception means.

[0015] As described above, the decoding means employed in theinformation reception apparatus provided by the present inventioncarries out a decoding process to produce at least one of the firstinformation-bit sequence and the second information-bit sequence on thebasis of a received value comprising an additive encoded sequence and apredetermined noise added to the additive encoded sequence produced bythe addition means, which adds a first constant-times encoded sequenceproduced by the first multiplication means as a result of amultiplication process to a second constant-times encoded sequenceproduced by the second multiplication means as a result of amultiplication process.

[0016] In addition, in accordance with the present invention, whichachieves above-described object, there is provided an informationtransmission method, which is used for receiving a reception signalcomprising an additive encoded sequence and a predetermined noise addedto the additive encoded sequence transmitted in accordance with aninformation transmission method including: a first conversion process ofconverting a first information-bit sequence comprising a predeterminednumber of bits into a first encoded sequence comprising M numbers; afirst multiplication process of multiplying the first encoded sequenceproduced by the first conversion process as a result of conversion by afirst constant; at least a second conversion process of converting asecond information-bit sequence comprising a predetermined number ofbits into a second encoded sequence comprising M numbers; at least asecond multiplication process of multiplying the second encoded sequenceproduced by the second conversion process as a result of conversion by asecond constant; an addition process of adding the constituent of afirst constant-times encoded sequence produced by the firstmultiplication process as a result of multiplication to the constituentof a second constant-times encoded sequence produced by the secondmultiplication process as a result of multiplication to produce anadditive encoded sequence; and a transmission process of transmittingthe additive encoded sequence as the transmitted signal, wherein theinformation reception method is characterized in that the informationreception method includes: a reception process of inputting thereception signal; and a decoding process of carrying out a decodingprocess to produce at least one of the first information-bit sequenceand the second information-bit sequence on the basis of a received valuereceived from the reception process.

[0017] As described above, in the information reception method providedby the present invention carries out the decoding process to produce atleast one of the first information-bit sequence and the secondinformation-bit sequence on the basis of a received value comprising anadditive encoded sequence and a predetermined noise added to theadditive encoded sequence, in the addition process carried out to add afirst constant-times encoded sequence produced in the firstmultiplication process to a second constant-times encoded sequenceproduced in the second multiplication process.

BRIEF DESCRIPTION OF DRAWINGS

[0018]FIG. 1 is an explanatory diagram showing a definition of anencoding process in the present invention;

[0019]FIG. 2 is an explanatory diagram showing locations of signalpoints in a constant-times encoded sequence produced in the encodingprocess carried out by a transmission apparatus of a data transmissionand reception system implemented by an embodiment of the presentinvention;

[0020]FIG. 3 is an explanatory diagram showing locations of signalpoints in an additive encoded sequence produced as a result of summingup 2 constant-times encoded sequences in the encoding process carriedout by the transmission apparatus of the same data transmission andreception system;

[0021]FIG. 4 is an explanatory diagram showing locations of signalpoints in an additive encoded sequence produced as a result of summingup 3 constant-times encoded sequences in the encoding process carriedout by the transmission apparatus of the same data transmission andreception system;

[0022]FIG. 5 is an explanatory diagram showing locations of signalpoints produced by adoption of an ordinary 4ASK modulation technique;

[0023]FIG. 6 is an explanatory diagram showing locations of signalpoints obtained for a signal-to-noise ratio of 12 dB;

[0024]FIG. 7 is an explanatory diagram showing locations of signalpoints obtained for a signal-to-noise ratio of 1.96 dB;

[0025]FIG. 8 is an explanatory diagram showing an enlarged portion ofsignal-point locations shown in FIG. 7, which is a portion in closeproximity to an area for an information amount of 1 bit;

[0026]FIG. 9 is a block diagram showing an actual and concreteconfiguration of the transmission apparatus of the same datatransmission and reception system;

[0027]FIG. 10 is a block diagram showing an a concrete configuration ofa converter employed in the transmission apparatus;

[0028]FIG. 11 is a block diagram showing an a concrete configuration ofan element encoder employed in the transmission apparatus;

[0029]FIG. 12 is a block diagram showing the configuration of anordinary reception apparatus for carrying out a decoding processaccording to the present invention;

[0030]FIG. 13 is a block diagram showing an actual and concreteconfiguration of the reception apparatus of the same data transmissionand reception system;

[0031]FIG. 14 is an explanatory block diagram showing the configurationof an ordinary turbo decoder;

[0032]FIG. 15 is an explanatory block diagram showing a concreteconfiguration of a decoder employed in the same reception apparatus;

[0033]FIG. 16 is an explanatory block diagram showing a configuration ofa channel estimation unit employed in the same reception apparatus or,to put it in detail, an explanatory block diagram showing theconfiguration of a channel estimation unit for finding ahard-decision-value sequence through the use of posteriori probabilityinformation for an information-bit sequence;

[0034]FIG. 17 is an explanatory block diagram showing anotherconfiguration of a channel estimation unit employed in the samereception apparatus or, to put it in detail, an explanatory blockdiagram showing the configuration of a channel estimation unit forfinding a hard-decision-value sequence through the use of posterioriprobability information for an information-bit sequence;

[0035]FIG. 18 is an explanatory block diagram showing a configuration ofa data transmission and reception system, in which the receptionapparatus identifies a state of a communication line as a part of anadaptive encoding process, in a plain and simple manner;

[0036]FIG. 19 is an explanatory block diagram showing a configuration ofa data transmission and reception system, in which the receptionapparatus identifies a state of a communication line as a part of anadaptive encoding process, in a plain and simple manner or, to put it indetail, an explanatory block diagram showing a configuration of a datatransmission and reception system, which gives an advance notice of anencoding-parameter change, in a plain and simple manner;

[0037]FIG. 20 is an explanatory block diagram showing a configuration ofa data transmission and reception system, in which the transmissionapparatus identifies a state of a communication line as a part of anadaptive encoding process, in a plain and simple manner or, to put it indetail, an explanatory block diagram showing a configuration of a datatransmission and reception system, in which the transmission apparatusincludes an encoding parameter of the current time in data of thecurrent time and transmits the current-time data including thecurrent-time encoding parameter to the reception apparatus, in a plainand simple manner;

[0038]FIG. 21 is an explanatory diagram showing the configuration ofcode used in a simulation for finding a characteristic in an AWGNchannel;

[0039]FIG. 22 is an explanatory diagram showing curves representingcharacteristics in an AWGN channel, which are found by the samesimulation;

[0040]FIG. 23 is an explanatory diagram showing the configuration ofcode used in a simulation for finding a characteristic in a freeinterleaved Rayleigh channel;

[0041]FIG. 24 is an explanatory diagram showing curves representingcharacteristics in a free interleaved Rayleigh channel, which are foundby the same simulation;

[0042]FIG. 25 is an explanatory diagram showing the configuration ofcode obtained as a result of estimating a characteristic in a staticchannel by using an encoding parameter for a Rayleigh channel; and

[0043]FIG. 26 is an explanatory diagram showing locations of signalpoints in an additive encoded sequence obtained by application of a QPSKmodulation technique as an encoding process carried out by a converteremployed in the same transmission apparatus.

BEST MODE FOR CARRYING OUT THE INVENTION

[0044] A concrete embodiment of the present invention is described indetail by referring to diagrams as follows.

[0045] This embodiment implements a data transmission and receptionsystem applied to a channel model in which digital information isencoded by a transmission apparatus shown in none of the figures and,then, the output of the transmission apparatus is transmitted to areception apparatus also shown in none of the figures by way of a noisytransmission line. In this data transmission and reception system, thetransmission apparatus is capable of forming a code having a largetransmission rate by using a code having a small transmission rate to bedescribed later. The transmission apparatus carries out an encodingprocess, which changes the concept of the existing signal-point mappingmethod. On the other hand, the reception apparatus of the datatransmission and reception system decodes codes, which have been encodedby the transmission apparatus, with ease and a high degree of precision.

[0046] First of all, before the data transmission and reception systemis explained, an encoding process of the present invention is defined asfollows.

[0047] The encoding process to be described below means the so-calledcommunication-line encoding process which can be interpreted inaccordance with a broad definition as a process to convert a signal ofexisting information for a given communication line. A most importantcommunication line is a communication line represented by Euclid's spaceto which a white Gaussian noise is added. In the field of datatransmission, problems such as a transmission speed [bits/s] and anoccupation band are normally raised. According to the sampling theorem,however, since a signal in 1 [s]×1 [Hz] can be described by using 2 realnumbers or 1 complex number, it is not necessary to consider the conceptof time or the concept of a frequency in the encoding process to bedescribed below. Instead, the concept can be replaced by the number ofdimensions in a vector space in a simple manner. That is to say, theencoding process to be described below can be defined as a process toconvert logic information consisting of N bits into an encoded sequenceof M numbers used as 2^(N) code words.

[0048] A parameter called a transmission rate C can be defined in termsof N and M as shown in Eq. (1) given below where symbol N is the numberof bits composing the logic information to be converted and symbol M isthe number of dimensions of a conversion-result vector space.

C=N/M  (1)

[0049] That is to say, the transmission rate C is the number of bitstransmitted per real-number dimension. In the encoding theory, anencoding rate R is defined by Eq. (2) given below where symbols k and ndenote the number of information bits and a code length respectively.For a case where 1 code bit is mapped onto 1 real number as is the casewith a BPSK (Binary Phase Shift Keying) modulation technique, thetransmission rate C is equal to a coding rate R.

R=k/n  (2)

[0050] When considering a general encoding process including theso-called coded modulation, the transmission rate C can be said to be aparameter more meaningful than the encoding rate R in many cases whencompared with the encoding rate R. As a parameter having a dimensionequivalent to the transmission rate C, there is a transmission speed Uper frequency cycle [bits/Hz]. In accordance with the sampling theorem,since 2 real numbers per Hz are transmitted in each unit time, thetransmission rate C and the transmission speed U satisfy a relationexpressed by Eq. (3) given below. Since neither the time concept nor thefrequency concept is required in the encoding process as describedabove, even in comparison with the transmission speed U, thetransmission rate C can be said to be a parameter more meaningful thanthe transmission speed U.

C=U/2  (3)

[0051] In this case, a maximum communication-line capacity C_(max)[bits] in C. E. Shannon's communication-line encoding theorem isexpressed by Eq. (4) as follows: $\begin{matrix}{C_{\max} = {\frac{1}{2}{\log_{2}\left( {1 + \frac{S}{N}} \right)}}} & (4)\end{matrix}$

[0052] Eq. (4) given above means that, in a communication line to whichan Additive White Gaussian Noise is added to result in an asignal-to-noise ratio S/N, information of C_(max) bits can betransmitted per real number without introducing errors. In addition,energy of inform per bit is normally expressed by E_(b) [J]. That is tosay, in a transmission of information of C_(max) bits per real number,the energy per real number is expressed by C_(max)·E_(b) [J]. Theadditive white Gaussian noise is referred to hereafter as an AWGN. In anAWGN channel of a noise power density n_(o) [j], the energy of an addednoise per real number is n_(o)/2 [J]. Thus, as a limit of acommunication line capacity, the maximum communication-line capacityC_(max) is expressed by Eq. (5) as follows: $\begin{matrix}{C_{\max} = {\frac{1}{2}{\log_{2}\left( {1 + {2\quad C_{\max}\frac{E_{b}}{n_{0}}}} \right)}}} & (5)\end{matrix}$

[0053] On the other hand, let symbol min denote the minimum value of asignal-to-noise power ratio E_(b)/n_(o) per bit, which is a minimumpower ratio required for transmitting information of C bits per realnumber. In this case, a communication rate C [bits] is expressed by Eq.(6) given below. From this equation, it is possible to derive Eq. (7)expressing the minimum value of a signal-to-noise power ratioE_(b)/n_(o) per bit ξ_(min). $\begin{matrix}{C = {\frac{1}{2}{\log_{2}\left( {1 + {2\quad C\quad \xi_{\min}}} \right)}}} & (6) \\{\xi_{\min} = {\frac{1}{2\quad C}\left\lbrack {2^{2C} - 1} \right\rbrack}} & (7)\end{matrix}$

[0054] The following description explains a data transmission andreception system including a transmission apparatus for carrying out theencoding process defined as described above and a reception apparatusfor decoding codes obtained as a result of the encoding process carriedout by the transmission apparatus.

[0055] First of all, the transmission apparatus included in the datatransmission and reception system is described. By using a code with asmall transmission rate described above, the transmission apparatuscreates a code with a large sequential transmission rate. Here, in thefirst place, before an actual and concrete configuration of thetransmission apparatus is explained, the basic principle of the encodingprocess carried out by the transmission apparatus is described.

[0056] There are L information-bit sequences {b⁽⁰⁾, b⁽¹⁾, . . . ,b^((L−1))}. As indicated by Eq. (8) given below, the firstinformation-bit sequence b⁽¹⁾ comprises N information bits b_(n) ⁽¹⁾where n=0, 1, . . . and N−1. $\begin{matrix}{b_{n}^{(l)} = \left\{ {b_{0}^{(l)},{b_{2}^{(l)}\quad \ldots}\quad,b_{N - 1}^{(l)}} \right\}^{T}} & (8)\end{matrix}$

[0057] Consider a real-number-value sequence x⁽¹⁾ shown in Eq. (9)below. The real-number-value sequence x⁽¹⁾ is obtained as a result of anencoding process to map the information bits b_(n) ⁽¹⁾ expressed by Eq.(8) given above for each information-bit sequence. It should be notedthat the real-number-value sequence x⁽¹⁾ is referred to hereafter as anencoded sequence x⁽¹⁾.

x ⁽¹⁾ =x ⁽¹⁾(b ⁽¹⁾)  (9)

[0058] The encoded sequence x⁽¹⁾ is an M-dimensional real-number vectorconsisting of M real numbers without regard to the sequence as indicatedby Eq. (10) given below. $\begin{matrix}{x^{(l)} = \left\{ {x_{0}^{(l)},{x_{1}^{(l)}\quad \ldots}\quad,x_{N - 1}^{(l)}} \right\}^{T}} & (10)\end{matrix}$

[0059] In this case, a transmission rate C⁽¹⁾ is expressed by Eq. (11)as follows:

C ⁽¹⁾ =N ⁽¹⁾ M  (11)

[0060] Let symbol ξ⁽¹⁾ denote a minimum value of a signal-to-noise powerratio E_(b)/n_(o) per bit, which is a minimum value required for settinga transmission-error rate at 0 or a value close to 0 in the encodingprocess. In addition, in order to make the following explanation easy todescribe, assume that a code x forms an M-dimensional Gaussiandistribution as expressed by Eq. (12) given below. $\begin{matrix}{{p\left( x^{(l)} \right)} = {\frac{1}{\left( {2\pi \quad C^{(l)}E_{b}} \right)^{\frac{M}{2}}}{\exp \left\lbrack {{- \frac{1}{2C^{(l)}E_{b}}}{x^{(l)}}^{2}} \right\rbrack}}} & (12)\end{matrix}$

[0061] An encoded sequence x⁽⁰⁾ is obtained as a result of an encodingprocess carried out on an information-bit sequence b⁽⁰⁾ as expressed bythe following equation: x⁽⁰⁾=x⁽⁰⁾(b⁽⁰⁾). Energy per bit E_(b) ⁽⁰⁾ [J]required for accurately transmitting the encoded sequence x⁽⁰⁾ throughan AWGN channel having a noise power density no [J] is 2ξ times thevariance n_(o)/2 of a noise per real number as shown in Eq. (13) givenbelow.

E _(b) ⁽⁰⁾=2ξ⁽⁰⁾ n ₀/2=ξ⁽⁰⁾ n ₀  (13)

[0062] In this case a signal variance ν⁽⁰⁾ per real number is found byusing Eq. (14) as follows.

ν⁽⁰⁾ =C ⁽⁰⁾ξ⁽⁰⁾ n ₀  (14)

[0063] Consider a case in which an encoded sequence x⁽¹⁾ is added to thetransmission system and transmitted with a high degree of accuracy. Inthis case, the encoded sequence x⁽¹⁾ is obtained as a result of anencoding process carried out on an information-bit sequence b⁽¹⁾ asexpressed by the following equation: x⁽¹⁾=x⁽¹⁾(b⁽¹⁾) The encodedsequence x⁽⁰⁾ has nothing to do with the encoded sequence x⁽¹⁾. That isto say, the encoded sequence x⁽⁰⁾ merely appears as a noise to theencoded sequence x⁽¹⁾. Thus, as shown in Eq. (15) given below, energyper bit E_(b) ⁽¹⁾ [J] required for accurately transmitting the encodedsequence x⁽¹⁾ is set at a value ξ⁽¹⁾ times the sum of energies of anoriginal noise and the code x⁽¹⁾.

E _(b) ⁽¹⁾=2ξ⁽¹⁾(n ₀2/+C ⁽⁰⁾ξ⁽⁰⁾ n ₀)=n ₀ξ⁽¹⁾(1+2C ⁽⁰⁾ξ⁽⁰⁾  (15)

[0064] In this case, a signal variance ν⁽¹⁾ per real number is found byusing Eq. (16) as follows.

ν⁽¹⁾ =C ⁽¹⁾ξ⁽¹⁾ n ₀(1+2C ⁽⁰⁾ξ⁽⁰⁾)  (16)

[0065] In addition, by the same token, consider a case in which anencoded sequence x⁽²⁾ is added to the transmission system andtransmitted with a high degree of accuracy. In this case, the encodedsequence x⁽²⁾ is obtained as a result of an encoding process carried outon an information-bit sequence b⁽²⁾ as expressed by the followingequation: x⁽²⁾=x⁽²⁾(b⁽²⁾) The encoded sequences x⁽⁰⁾ and x⁽¹⁾ havenothing to do with the encoded sequence x⁽²⁾ That is to say, the encodedsequences x⁽⁰⁾ and x⁽¹⁾ merely appear as noises to the encoded sequencex⁽²⁾. Thus, as shown in Eq. (17) given below, energy per bit E_(b) ⁽²⁾[J] required for accurately transmitting the encoded sequence x⁽²⁾ isset at a value ξ⁽²⁾ times the sum of energies of an original noise andthe codes x⁽⁰⁾ and x⁽¹⁾. In this case a signal variance ν⁽²⁾ per realnumber is found by using Eq. (18) as follows. $\begin{matrix}\begin{matrix}{E_{b}^{(2)} = {2\quad \xi^{(2)}\left\{ {{n_{0}/2} + {C^{(0)}\xi^{(0)}n_{0}} + {C^{(l)}\xi^{(l)}{n_{0}\left( {1 + {2C^{(0)}\xi^{(0)}}} \right)}}} \right\}}} \\{= {\xi^{(2)}{n_{0}\left( {1 + {2C^{(0)}\xi^{(0)}}} \right)}\left( {1 + {2C^{(l)}\xi^{(l)}}} \right)}}\end{matrix} & (17)\end{matrix}$

 ν⁽²⁾ =C ⁽²⁾ξ⁽²⁾ n ₀(1+2C ⁽⁰⁾ξ⁽⁰⁾)(1+2C ⁽¹⁾ξ⁽¹⁾)  (18)

[0066] Thereafter, the same operation is carried out repeatedly on thesubsequent information-bit sequences ending with the information-bitsequence b^((L−1)). As a result, energy per bit E_(b) ^((L−1)) [J]required for accurately transmitting the encoded sequence x^((L−1)) isexpressed by Eq. (19) given below. In this case a signal varianceν^((L−1)) per real number is found by using Eq. (20) as follows.$\begin{matrix}{E_{b}^{({L - 1})} = {\xi^{({L - 1})}n_{0}{\prod\limits_{l = 0}^{L - 2}\quad \left( {1 + {2C^{(l)}\xi^{(l)}}} \right)}}} & (19) \\{v^{({L - 1})} = {C^{({L - 1})}\xi^{({L - 1})}n_{0}{\prod\limits_{l = 0}^{L - 2}\quad \left( {1 + {2C^{(l)}\xi^{(l)}}} \right)}}} & (20)\end{matrix}$

[0067] The above operations are carried out on one transmission systemto give an average amplitude a^((i)) for the information-bit sequences.In this case, encoded sequences for the information-bit sequences {b⁽⁰⁾,b⁽¹⁾, . . . , b^((L−1))} are expressed by Eqs. (21) and (22) as follows:$\begin{matrix}{{g\left( {b^{(0)},b^{(1)},\quad \ldots \quad,b^{({L - 1})}} \right)} = {{\sum\limits_{i = 0}^{L - 1}\quad {a^{(i)}x^{(i)}}} = {{a^{(0)}x^{(0)}} + {a^{(1)}x^{(1)}} + \ldots + {a^{({L - 1})}x^{({L - 1})}}}}} & (21) \\{a^{(i)} = {\sqrt{\frac{v^{(i)}}{n_{0}/2}} = \sqrt{2\quad C^{({L - 1})}\xi^{({L - 1})}{\prod\limits_{i = 0}^{L - 2}\quad \left( {1 + {2C^{(i)}\xi^{(i)}}} \right)}}}} & (22)\end{matrix}$

[0068] It should be noted that, in the following description, a sequenceobtained as a result of multiplying each constituent of the encodedsequence by a constant a⁽¹⁾ is referred to as a constant-times encodedsequence, and encoded sequences g (b⁽⁰⁾, b⁽¹⁾, . . . , b^((L−1))) areeach referred to as an additive encoded sequence. It is also worthnoting that the additive encoded sequences g(b⁽⁰⁾, b⁽¹⁾, . . . ,b^((L−1))) can also each be a complex-number-value sequence obtained bycombining every two constituents of a numerical-value sequence.

[0069] On the basis of such a principle, the transmission apparatuscarries out conversion processing including an encoding process and/or amodulation process on the input information-bit sequences {b⁽⁰⁾, b⁽¹⁾, .. . , b^((L−1))} to generate the additive encoded sequences g(b⁽⁰⁾,b⁽¹⁾, . . . , b^((L−1))), and transmits the additive encoded sequencesg(b⁽⁰⁾, b⁽¹⁾, . . . , b^((L−1))) to a communication line. To put it indetail, the transmission apparatus carries out a predeterminedconversion process on each of the input information-bit sequences {b⁽⁰⁾,b⁽¹⁾, . . . , b^((L−1))} to generate encoded sequences {x⁽⁰⁾, x⁽¹⁾, . .. , x^((L−1))}, and multiplies the encoded sequences {x⁽⁰⁾, x⁽¹⁾, . . ., x^((L−1))} by constants {a⁽⁰⁾, a⁽¹⁾, . . . , a^((L−1))} respectively.Then, constant-times encoded sequences obtained as a result of themultiplication are summed up to produce the additive encoded sequencesg(b⁽⁰⁾, b⁽¹⁾, . . . b^((L−1))).

[0070] In this case, as shown in Eq. (22) given above, the transmissionapparatus sets the constants a⁽⁰⁾, a⁽¹⁾, . . . , a^((L−1)) at suchvalues that the encoded sequence x⁽¹⁾ is transmitted through thecommunication line described below with a high degree of accuracy, thatis, at a sufficiently reduced bit error rate for the information-bitsequence b⁽¹⁾. Along the communication line, a sum of noises and aspecific sequence is added. The specific sequence has the samestatistical properties as the constant-times encoded sequences a⁽⁰⁾x⁽⁰⁾,a⁽¹⁾x⁽¹⁾, . . . , a^((L−1))x^((L−1)) summed up previously. Theconstant-times encoded sequences a⁽⁰⁾x⁽⁰⁾, a⁽¹⁾x⁽¹⁾, . . . ,a^((L−1))x^((L−1)) are obtained as a product of multiplying the encodedsequences x⁽¹⁾ by the constants a⁽¹⁾. It should be noted that thestatistical properties of the constant-times encoded sequence a⁽¹⁾x⁽¹⁾include a variance, a probability density function and a power spectrum.

[0071] To put it concretely, on the assumption that the encoded sequencex⁽⁰⁾ is transmitted through a communication line adding a noise, theconstant a⁽⁰⁾ is set at such a value that the bit error rate for theinformation-bit sequence b⁽⁰⁾ is reduced sufficiently. In addition, onthe assumption that the encoded sequence x⁽¹⁾ is transmitted through thecommunication line, along which a sum of a noise and a specific sequenceis added, the constant a⁽¹⁾ is set at such a value that the bit errorrate for the information-bit sequence b⁽¹⁾ is reduced sufficiently. Thespecific sequence has the same statistical properties as theconstant-times encoded sequence a⁽⁰⁾x⁽⁰⁾. Furthermore, on the assumptionthat the encoded sequence x⁽²⁾ is transmitted through the communicationline, along which a sum of a noise and another specific sequence isadded, the constant a⁽²⁾ is set at such a value that the bit error ratefor the information-bit sequence b⁽²⁾ is reduced sufficiently. The otherspecific sequence has the same statistical properties as theconstant-times encoded sequences a⁽⁰⁾x⁽⁰⁾ and a⁽¹⁾x⁽¹⁾.

[0072] In this case, it is possible to find a criterion for determiningwhether or not the bit error rate for the information-bit sequence b⁽¹⁾is reduced sufficiently by logical consideration or simulation. It is tobe noted that, as a sufficiently small bit error rate, a value smallerthan a bit error rate required eventually in the system is appropriate.A typical sufficiently small bit error rate of about 10⁻⁵ is desirable.

[0073] As described above, while providing equal weights to theinformation-bit sequences b⁽¹⁾, the transmission apparatus is capable ofsetting the constants a⁽¹⁾.

[0074] In addition, the transmission apparatus may set the constantsa⁽¹⁾ by changing margins for noises for each code.

[0075] That is to say, the transmission apparatus sets a constant a⁽¹⁾to be used as a multiplicand for any encoded sequence x⁽¹⁾ at such avalue that the encoded sequence x⁽¹⁾ is transmitted through thecommunication line described below with a high degree of accuracy, thatis, at a sufficiently reduced bit error rate for the information-bitsequence b⁽¹⁾. Along the communication line, a sum of a noise and aspecific sequence is added. The noise is greater than an assumed noiseby G⁽¹⁾ [dB]. The specific sequence has the same statistical propertiesas the constant-times encoded sequences a⁽⁰⁾x⁽⁰⁾, a⁽¹⁾x⁽¹⁾, . . . ,a⁽¹⁻¹⁾x⁽¹⁻¹⁾ summed up previously.

[0076] To put it concretely, on the assumption that the encoded sequencex⁽⁰⁾ is transmitted through a communication line adding a noise, theconstant a⁽⁰⁾ is set at such a value that the bit error rate for theinformation-bit sequence b⁽⁰⁾ is reduced sufficiently. In addition, onthe assumption that the encoded sequence x⁽¹⁾ is transmitted through thecommunication line, along which a sum of a noise and a specific sequenceis added, the constant a⁽¹⁾ is set at such a value that the bit errorrate for the information-bit sequence b⁽¹⁾ is reduced sufficiently. Thenoise is greater than an assumed noise by G⁽¹⁾ [dB]. The specificsequence has the same statistical properties as the constant-timesencoded sequence a⁽⁰⁾x⁽⁰⁾. Furthermore, on the assumption that theencoded sequence x⁽²⁾ is transmitted through the communication line,along which a sum of a noise and another specific sequence is added, theconstant a⁽²⁾ is set at such a value that the bit error rate for theinformation-bit sequence b⁽²⁾ is reduced sufficiently. The noise isgreater than an assumed noise by G⁽¹⁾ [dB]. The other specific sequencehas the same statistical properties as the constant-times encodedsequences a⁽⁰⁾x⁽⁰⁾ and a⁽¹⁾x⁽¹⁾.

[0077] As described above, the transmission apparatus is capable ofsetting the constants a⁽¹⁾ with ease while changing a weight for eachinformation-bit sequence b⁽¹⁾. As will be described later, this methodof setting the constants a⁽¹⁾ is effective for a case in which theimportance of each information-bit sequence b⁽¹⁾ varies. The moreimportant the information-bit sequence b⁽¹⁾, the larger the value atwhich the constant a⁽¹⁾ is set.

[0078] It should be noted that, even if the transmission apparatustransmits the encoded sequence x⁽¹⁾ through different communicationlines as is the case with a Rayleigh fading channel, the constants a⁽¹⁾can be set by carrying out the same operations as the method describedabove. A criterion as to whether or not a bit error rate for theinformation-bit sequence b⁽¹⁾ is reduced sufficiently can be based on aresult of a study or a simulation using an assumed channel model. Thisis because energy E_(b) [J] required for implementing a desired biterror rate varies in accordance with the state of the communicationline. In addition, as will be described later, it is possible to set theconstant a⁽¹⁾ adaptive to a change in communication-line state.

[0079] Anyway, in order to transmit an information-bit sequence b⁽¹⁾ byexpending energy E_(b) [J] required for implementing a desired bit errorrate, the transmission apparatus multiplies an encoded sequence x⁽¹⁾ bya constant a⁽¹⁾.

[0080] Consider a signal-point location of an additive encoded sequenceg obtained as a result of an encoding process carried out by thetransmission apparatus. It should be noted that, in order to make thefollowing explanation easy to describe, in an operation to generate anencoded sequence x⁽¹⁾ a signal-point mapping process based on the BPSKmodulation technique is carried out.

[0081] Since the encoded sequence x⁽⁰⁾ has been subjected to the BPSKmodulation technique, the signal points are located at coordinates “1”and “−1” on the I axis of the so-called IQ plane. Thus, for theconstant-times encoded sequence a⁽⁰⁾x⁽⁰⁾, the signal points are locatedat coordinates “a⁽⁰⁾” and “−a⁽⁰⁾” on the I axis as shown by blackcircles in FIG. 2. It is needless to say that the absolute value of thecoordinate “a⁽⁰⁾” varies in dependence on the sequence.

[0082] Thus, there are 4(=2²) signal-point locations of the additiveencoded sequence a⁽⁰⁾x⁽⁰⁾+a⁽¹⁾x⁽¹⁾ obtained as a sum of theconstant-times encoded sequence a⁽⁰⁾x⁽⁰⁾ and the constant-times encodedsequence a⁽¹⁾x⁽¹⁾ which are obtained by adoption of the BPSK modulationtechnique, as shown by black circles on the I axis in FIG. 3 similarlyto those of an Amplitude Shift Keying modulation technique. TheAmplitude Shift Keying modulation technique is referred to hereafter asthe ASK modulation technique. By the same token, there are 8(=2³)signal-point locations of the additive encoded sequencea⁽⁰⁾x⁽⁰⁾+a⁽¹⁾x⁽¹⁾+a⁽²⁾x⁽²⁾ obtained as a sum of the constant-timesencoded sequence a⁽⁰⁾x⁽⁰⁾, the constant-times encoded sequence a⁽¹⁾x⁽¹⁾and the constant-times encoded sequence a⁽²⁾x⁽²⁾ as shown by blackcircles on the I axis in FIG. 4 similarly to those of the ASK modulationtechnique. Finally, there are 2^(L) signal-point locations of theadditive encoded sequence g (=a⁽⁰⁾x⁽⁰⁾+a⁽¹⁾x⁽¹⁾+a⁽²⁾x⁽²⁾+ . . .+a^((L−1))x^((L−1))) obtained as a sum of the constant-times encodedsequence a⁽⁰⁾x⁽⁰⁾, the constant-times encoded sequence a⁽¹⁾x⁽¹⁾ theconstant-times encoded sequence a⁽²⁾x⁽²⁾, . . . and the constant-timesencoded sequence a^((L−1))x^((L−1)) as shown by black circles on the Iaxis in FIG. 4 similarly to those of the ASK modulation technique.

[0083] In the ordinary ASK modulation technique, there are signal pointslocated at equal intervals as is the case with a 4ASK modulationtechnique shown in FIG. 5. In the proposed encoding process, however,the constant a⁽¹⁾ is set at such a value that the information-bitsequence b⁽¹⁾ is transmitted by expending energy E_(b) [J] forimplementing a desired bit error rate as described above, and signalpoints are located on the basis of the constant a⁽¹⁾. In this case, thesignal points of the additive encoded sequence g are not necessarilylocated at equal intervals. Rather, the signal points are located atunequal intervals as shown in FIGS. 3 and 4. The validity of thisstatement is explained by using the 4ASK modulation technique as anexample.

[0084] In order to feel for the inevitability of signal points' beinglocated at unequal intervals, the signal points in the 4ASK modulationtechnique are given as shown in Eq. (23) given below. Then, x is changedto find the amount of information. In this case, the variation becomesequal to 1.

{x ₀ ,x ₁ ,x ₂ ,x ₃}={{square root}{square root over (2−^(x)²)},x,−x,−{square root}{square root over (2−x ²)}}  (23)

[0085] For x!=1, the information amount H [bits] of a transmitted signalis 2 bits as expressed by Eq. (24) given below without the need tochange x. $\begin{matrix}{H = {{{- {\sum\limits_{i = 0}^{3}\quad {{P\left( x_{i} \right)}{\log \left( {P\left( x_{i} \right)} \right)}}}} - {\sum\limits_{i = 0}^{3}\quad {\frac{1}{4}{\log \left( \frac{1}{4} \right)}}}} = 2}} & (24)\end{matrix}$

[0086] If the communication line is an AWGN channel having a noise powerdensity n_(o), on the other hand, the amount of information received bythe reception apparatus is expressed by Eq. (25) given below wheresymbol y denotes a reception value. It should be noted that expression“p(y|x_(i))” used in Eq. (25) is represented by Eq. (26) given below.$\begin{matrix}\begin{matrix}{{I\left( {x,y} \right)} = {{H(y)} - {H\left( {{y\left. x \right)} = {{H(y)} - {H(n)}}} \right.}}} \\{= {{- {\int_{- \infty}^{\infty}{{p(y)}{\log_{2}\left( {p(y)} \right)}\quad {y}}}} - {\frac{1}{2}{\log_{2}\left( {\pi \quad {en}_{0}} \right)}}}} \\{= {- {\int_{- \infty}^{\infty}{\sum\limits_{i = 0}^{3}\quad {p\left( {y\left. x_{i} \right){p\left( x_{i} \right)}{\log_{2}\left( {{\sum\limits_{i = 0}^{3}{{p\left( \quad {y\left. x_{i} \right){p\left( x_{i} \right)}} \right)}{y}}} - {\frac{1}{2}{\log_{2}\left( {\pi \quad {en}_{0}} \right)}}} \right.}} \right.}}}}}\end{matrix} & (25) \\{p\left( \quad {{y\left. x_{i} \right)} = {\frac{1}{\sqrt{\pi \quad n_{0}}}{\exp \left\lbrack {{- \frac{1}{n_{0}}}{{y - x_{i}}}^{2}} \right\rbrack}}} \right.} & (26)\end{matrix}$

[0087] The amounts of information for location of x with thesignal-to-noise ratio S/N set at 12 dB are calculated to give a curvehaving maximum values at 2 points as shown in FIG. 6. As is obvious fromthe figure, the amount of information is equal to a maximum value ofclose to 2 bits for x=1.34 and x=0.45. This state corresponds to theordinary 4ASK modulation technique for which signal points indicated byEq. (27) given below are located at equal intervals as shown in FIG. 7.Thus, the validity that the signal points are located at equal intervalsis proven. It should be noted that, as is also obvious from the figure,for x=1.0, the amount of information is equal to that of the BPSKmodulation technique, indicating that transmission of more than 1 bit isimpossible.

{x ₀ ,x ₁ ,x ₂ ,x ₃}={3/{square root}{square root over (5)},1/{squareroot}{square root over (5)},−3/{square root}{square root over(5)}}={1.34,0.45,−0.45,−1.34}  (27)

[0088] Then, from this state, the signal-to-noise ratio S/N is reducedto find a signal-to-noise ratio S/N for which a maximum amount ofinformation is 1 bit. That is to say, a state in which the transmissionrate C described earlier is 1.0. The amounts of information for locationof x with the signal-to-noise ratio S/N set at 1.96 dB are representedby a curve shown in FIG. 7. As shown in the figure, the amount ofinformation changes leniently in the range of values close to 1 bit withvariations in x. If a portion of the curve shown in the figure in anarea around an information amount of 1 bit is enlarged, a curve having amaximum value at 2 points as shown in FIG. 8 is obtained. As is obviousfrom the figure, the amount of information becomes equal to a maximumvalue for x=1.4 and x=0.2. It is also clear that signal pointsmaximizing the amount of information are located at equal intervals asindicated by Eq. (28) given below:

{x ₀ ,x ₁ ,x ₂ ,x ₃}={1.4,0.2,−0.2,−1.4}  (28)

[0089] These facts indicate that optimum signal-point locations aredetermined in dependence on the signal-to-noise ratio S/N. That is tosay, in this proposed encoding process, in processing to set a constanta⁽¹⁾ at such a value that an information-bit sequence b⁽¹⁾ istransmitted by expending energy E_(b) [J] for implementing a desired biterror rate, a mapping process with signal points located at unequalintervals results in improved characteristics more than the alreadyexisting mapping process with signal points located at equal intervalsdoes, making it unnecessary to adhere to the existing mapping process.It should be noted that, if the signal-to-noise ratio S/N is extremelylowered, the signal-point locations have been verified to be in a state,which can be said to be the so-called 3ASK modulation technique as shownby Eq. (29) as follows.

{x ₀ ,x ₁ ,x ₂ ,x ₃}={1.414,0.0,−0.0,−1.414}  (29)

[0090] In order to transmit an information-bit sequence b⁽¹⁾ byexpending energy E_(b) [J] for implementing a desired bit error rate,the transmission apparatus multiplies an encoded sequence x⁽¹⁾ by theconstant a⁽¹⁾ and sums up constant-times encoded sequences a⁽¹⁾ x⁽¹⁾each obtained as a result of the multiplication. In this way, anadditive encoded sequence g for which signal points are located atunequal intervals is generated. It is needless to say that, in somecases, the transmission apparatus generates an additive encoded sequenceg for which signal points are located at equal intervals. This indicatesthat optimum signal-point locations are determined in dependence on thesignal-to-noise ratio S/N as described above.

[0091] Let symbol C′ denote a total transmission rate for a transmissionof L information-bit sequences {b⁽⁰⁾, b⁽¹⁾, . . . , b^((L−1))}. In thiscase, the total transmission rate C′ is expressed by Eq. (30) asfollows: $\begin{matrix}{C^{\prime} = {\sum\limits_{i = 0}^{L - 1}\quad C^{(i)}}} & (30)\end{matrix}$

[0092] Let symbol E_(b.ave) [J] denote average energy per bit requiredby the information-bit sequences {b⁽⁰⁾, b⁽¹⁾, . . . , b^((L−1))} In thiscase, the average energy per bit E_(b.ave) [J] is expressed by Eq. (31)as follows: $\begin{matrix}\begin{matrix}{E_{b \cdot {ave}} = {\frac{\sum\limits_{i = 0}^{L - 1}\quad {N^{(l)}E_{b}^{(l)}}}{\sum\limits_{i = 0}^{L - 1}\quad N^{(l)}} = {\frac{\sum\limits_{i = 0}^{L - 1}{M\quad C^{(l)}E_{b}^{(l)}}}{\sum\limits_{i = 0}^{L - 1}{M\quad C^{(l)}}} = \frac{\sum\limits_{i = 0}^{L - 1}\quad {C^{(l)}E_{b}^{(l)}}}{\sum\limits_{i = 0}^{L - 1}\quad C^{(l)}}}}} \\{= {\frac{n_{0}}{C^{\prime}}{\sum\limits_{i = 0}^{L - 1}\quad {C^{(l)}\xi^{(l)}{\prod\limits_{i = 0}^{L - 1}\quad \left( {1 + {2C^{(i)}\xi^{(l)}}} \right)}}}}}\end{matrix} & (31)\end{matrix}$

[0093] Let symbol ξ_(ave) denote a minimum signal-to-noise power ratioE_(b.ave)/n_(o) per bit required to make an error rate equal to 0. Inthis case, this ξ_(ave′) is expressed by Eq. (32) as follows:$\begin{matrix}{\xi_{ave}^{\prime} = {\frac{1}{C^{\prime}}{\sum\limits_{i = 0}^{L - 1}\quad {C^{(l)}\xi^{(l)}{\prod\limits_{i = 0}^{l - 1}\quad \left( {1 + {2C^{(i)}\xi^{(i)}}} \right)}}}}} & (32)\end{matrix}$

[0094] In this case, the L encoded sequences {x⁽⁰⁾, x⁽¹⁾, . . . ,x^((L−1))} satisfy Shanon's limit equation, which is expressed by Eq.(33) as follows: $\begin{matrix}{\xi^{(i)} = {\frac{1}{2C^{(i)}}\left\lbrack {2^{2C^{(i)}} - 1} \right\rbrack}} & (33)\end{matrix}$

[0095] By substituting Eq. (33) into Eq. (32), Eq. (34) given below isobtained: $\begin{matrix}\begin{matrix}{\xi_{ave}^{\prime} = {\frac{1}{2C^{\prime}}{\sum\limits_{i = 0}^{L - 1}{\left( {2^{2C^{(i)}} - 1} \right){\prod\limits_{i = 0}^{L - 1}\left( 2^{2C^{(i)}} \right)}}}}} \\{= {{\frac{1}{2C^{\prime}}{\sum\limits_{i = 0}^{L - 1}{\left( {2^{2C^{(i)}} - 1} \right)2^{2{\sum\limits_{i = 0}^{L - 1}C^{(i)}}}}}} = {\frac{1}{2C^{\prime}}{\sum\limits_{i = 0}^{L - 1}\left( {2^{2{\sum\limits_{i = 0}^{L}C^{(i)}}} - 2^{2{\sum\limits_{i = 0}^{L - 1}C^{(i)}}}} \right)}}}} \\{= {\frac{1}{2C^{\prime}}\left( {2^{2{\sum\limits_{i = 0}^{L - 2}C^{(i)}}} - 2^{2{\sum\limits_{i = 0}^{L - 2}C^{(i)}}} + 2^{2{\sum\limits_{i = 0}^{L - 2}C^{(i)}}} - 2^{2{\sum\limits_{i = 0}^{L - 2}C^{(i)}}} + \ldots + 2^{2C^{(i)}} - 1} \right)}} \\{= {\frac{1}{2C^{\prime}}\left( {2^{2C^{\prime}} - 1} \right)}}\end{matrix} & (34)\end{matrix}$

[0096] The above indicates that, if the L encoded sequences {x⁽⁰⁾, x⁽¹⁾,. . . , x^((L−1))} satisfy Shanon's limit equation, code generatedeventually by the transmission apparatus also satisfies Shanon's limitequation as well.

[0097] As described above, the transmission apparatus is capable ofgenerating code that satisfies Shanon's limit equation.

[0098] Now, the following description explains details of an actualconcrete configuration of the transmission apparatus for carrying outthe encoding process described above. It should be noted that, in orderto make the following explanation easy to describe, the transmissionapparatus inputs 3 information-bit sequences {b⁽⁰⁾, b⁽¹⁾, b⁽²⁾}.

[0099] As shown in FIG. 9, for example, the transmission apparatus 10comprises 3 converters 10 ₀, 11 ₁ and 11 ₂, 3 multipliers 12 ₀, 12 ₁ and12 ₂, 2 adders 13 ₀ and 13 ₁ and a transmission unit 14. The converters11 ₀, 11 ₁ and 11 ₂ convert the information-bit sequences b^((i)) intoencoded sequences x^((i)). The multipliers 12 ₀, 12 ₁ and 12 ₂ multiplytheir respective encoded sequences x^((i)) output by the converters 11₀, 11 ₁ and 11 ₂ as results of the conversion processes by constantsa^((i)). The adder 13 ₀ adds a constant-times encoded sequence a⁽⁰⁾x⁽⁰⁾produced by the multiplier 12 ₀ as a result of multiplication to aconstant-times encoded sequence a⁽¹⁾x⁽¹⁾ produced by the multiplier 12 ₁as a result of multiplication. The adder 13 ₁ adds an additive encodedsequence a⁽⁰⁾x⁽⁰⁾+a⁽¹⁾x⁽¹⁾ produced by the adder 13 ₀ as a result ofaddition to a constant-times encoded sequence a⁽²⁾ x⁽²⁾ produced by themultiplier 12 ₂ as a result of multiplication. The transmission unit 14transmits an additive encoded sequence g(=a⁽⁰⁾x⁽⁰⁾+a⁽¹⁾x⁽ 1)+a⁽²⁾ x⁽ 2))produced by the adder 13 ₁ as a result of addition to an externalapparatus.

[0100] It should be noted that the input information-bit sequences{b⁽⁰⁾, b⁽¹⁾, b⁽²⁾} can be information transmitted through 3 channelsindependent of each other, or results of splitting an information-bitsequence into 3 sequences. In addition, the input information-bitsequences {b⁽⁰⁾, b⁽¹⁾, b⁽²⁾} can have an equal bit count or bit countsdifferent from each other, that is, N₀, N₁ and N₂.

[0101] The converters 11 ₀, 11 ₁ and 11 ₂ each have an encoder and amodulator, which are not shown in the figure. The converter 11 ₀converts the input information-bit sequences b⁽⁰⁾ having the bit countN₀ into a signal consisting of “1” and “−1” in Euclid's space. By thesame token, the converter 11 ₁ converts the input information-bitsequences b⁽¹⁾ having the bit count N₁ into such a signal. In the sameway, the converter 11 ₂ converts the input information-bit sequencesb⁽²⁾ having the bit count N₂ into such a signal. The converters 11 ₀, 11₁ and 11 ₂ may each carry out any encoding and modulation processes asthe conversion processing. It is even possible to go so far as to saythat the input information-bit sequences b⁽⁰⁾, b⁽¹⁾, b⁽²⁾ can be merelymodulated without carrying out an encoding process. At any rate, theconverters 11 ₀, 11 ₁ and 11 ₂ convert respectively the inputinformation-bit sequences b⁽⁰⁾, b⁽¹⁾, b⁽²⁾ having bit counts N₀, N₁ andN₂ respectively each into an encoded sequence consisting of M numbers.

[0102] As shown in FIG. 10, typically, the converters 11 ₀, 11 ₁ and 11₂ each comprise components for conceivably implementing a PCCC (ParallelConcatenated Convolutional Codes) encoding technique and a BPSK (BinaryPhase Shift Keying) modulation technique. The PCCC encoding technique isadopted to produce the so-called turbo codes.

[0103] As shown in the same figure, the converter 11 _(j) comprises 2element encoders 21 ₀ and 21 ₁, an interleaver 22, a puncture unit 23, achannel interleaver 24 and a BPSK mapper 25. The element encoders 21 ₀and 21 ₁ each carry out a convolution process. The interleaver 22rearranges the order of pieces of input data. The puncture unit 23carries out a proper discrete reduction process on input data. Thechannel interleaver 24 used for a channel rearranges the order of piecesof input data. The mapper 25 carries out a mapping process on signalpoints by adoption of the BPSK modulation technique.

[0104] The element encoders 21 ₀ and 21 ₁ are each designed to carry outtypically a recursive convolution process. The element encoders 21 ₀ and21 ₁ can be identical with each other or different from each other. Theelement encoders 21 ₀ and 21 ₁ can each be an element encoder 21 _(j)like one shown in FIG. 11. As shown in the figure, the element encoder21 _(j) conceivably comprises 2 exclusive-or circuits 31 ₀ and 31 ₁ and2 shift registers 32 ₀ and 32 ₁.

[0105] The exclusive-or circuit 31 ₀ carries out an exclusive-or processon data input to the element encoder 21 _(j), and pieces of datareceived from the shift registers 32 ₀ and 32 ₁. The data input to theelement encoder 21 _(j) is information bits b_(n) ^((i)) composing theinformation-bit sequence b^((i)) delayed by a time equal in length to aprocessing time of the interleaver 22. As an alternative, the input tothe element encoder 21 _(j) is interleaved data received from theinterleaver 22. A result of the exclusive-or process is supplied to theexclusive-or circuit 31 ₁ and the shift register 32 ₀.

[0106] The exclusive-or circuit 31 ₁ carries out an exclusive-or processon the data received from the exclusive-or circuit 31 ₀ and datareceived from the shift register 32 ₁, producing a result as output datato the external component.

[0107] The shift register 32 ₀ supplies 1-bit data held therein to theexclusive-or circuit 31 ₀ and the shift register 32 ₁. The shiftregister 32 ₀ then holds new 1-bit data, which is received from theexclusive-or circuit 31 ₀, synchronously with a clock signal. Then, theshift register 32 ₀ newly supplies the new 1-bit data held therein tothe exclusive-or circuit 31 ₀ and the shift register 32 ₁.

[0108] Subsequently, the shift register 32 ₁ again supplies 1-bit dataheld therein to the exclusive-or circuit 31 ₀ and the shift register 31₁. The shift register 32 ₀ then holds new 1-bit data, which is receivedfrom the exclusive-or circuit 31 ₀, synchronously with a clock signal.Then, the shift register 32 ₀ newly supplies the new 1-bit data heldtherein to the exclusive-or circuit 31 ₀ and the shift register 31 ₁.

[0109] When the element encoder 21 ₀, which is the element encoder 21_(j) described above, receives the information-bit sequence b_(n) ^((i))the element encoder 21 ₀ carries out a convolution process on theinformation bits b_(n) ^((i)). A result of the convolution process issupplied to the puncture unit 23 at the next stage as 1-bit output dataDa. Much like the element encoder 21 ₀, when the element encoder 21 ₁receives interleaved data Db from the interleaver 22, the elementencoder 21 ₁ carries out a convolution process on each bit of theinterleaved data Db. A result of the convolution process is supplied tothe puncture unit 23 at the next stage as 1-bit output data Dc.

[0110] The interleaver 22 receives the information-bit sequence b^((i))and rearranges the order of the information bits b_(n) ^((i)) composingthe information-bit sequence b^((i)) on the basis of information onpermutation locations, which is stored in a memory in advance, togenerate the interleaved data Db. The interleaver 22 then supplies theinterleaved data Db to the element encoder 21 ₁.

[0111] The puncture unit 23 carries out a discrete reduction process byalternatively selecting the 2 sequences of output data Da and Dc, whichare received from the element encoders 21 ₀ and 21 ₁ respectively, onthe basis of a predetermined rule. A result of the discrete reductionprocess is supplied to the channel interleaver 24 as puncture data Ddwith some bits thereof deleted.

[0112] The channel interleaver 24 receives the information-bit sequenceb^((i)) and the puncture data Dd generated by the puncture unit 23. Theinformation-bit sequence b^((i)) received by the channel interleaver 24has been delayed by a time equal in length to the sum of processingtimes required by the element encoder 21 ₁, the interleaver 22 and thepuncture unit 23. The channel interleaver 24 changes the orders of theinformation bits b_(n) ^((i)) composing the information-bit sequenceb^((i)) and the bits composing the puncture data Dd on the basis ofinformation on permutation locations, which is stored in a memory inadvance, to generate interleaved data De consisting of M bits. Thechannel interleaver 24 then supplies the interleaved data De to the BPSKmapping unit 25. It should be noted that the channel interleaver 24 isnot absolutely required. Typically, the channel interleaver 24 isprovided for the main purpose of improving a characteristic bydispersion of a burst error.

[0113] The BPSK mapping unit 25 synchronizes the interleaved data Dereceived from the channel interleaver 24 to the clock signal, mappingthe synchronized interleaved data De onto transmission symbols of theBPSK modulation technique. The BPSK mapping unit 25 outputs thegenerated transmission symbols to the external component as an encodedsequence x^((i)).

[0114] When the converter 11 _(j) described above receives aninformation-bit sequence b^((i)), the information-bit sequence b^((i))is supplied to the channel interleaver 24 as organization constituentdata. In addition, the output data Da obtained as a result of theconvolution process carried out by the element encoder 21 ₀ on theinformation-bit sequence b^((i)) and the output data Dc obtained as aresult of the convolution process carried out by the element encoder 21₁ on the interleaved data Db are supplied to the channel interleaver 24.Then, the converter 11 _(j) maps the interleaved data De ontotransmission symbols of the BPSK modulation technique and outputs thegenerated transmission symbols to the external component as an encodedsequence x^((i)).

[0115] Hereafter, in order to make the following explanation easy todescribe, the converters 11 ₀, 11 ₁ and 11 ₂ are assumed to each havethe same configuration as the converter 11 _(j) shown in the figure.

[0116] The converter 11 ₀ having a configuration identical with theconverter 11 _(j) described above converts an information-bit sequenceb⁽⁰⁾ consisting of N₀ input bits into M numerical values located in anM-dimensional real-number vector space, and supplies an encoded sequencex⁽⁰⁾ composed of the M numerical values to the multiplier 12 ₀. By thesame token, the converter 11 ₁ also having a configuration identicalwith the converter 11 _(j) described above converts an information-bitsequence b⁽¹⁾ consisting of N₁ input bits into M numerical valueslocated in the M-dimensional real-number vector space, and supplies anencoded sequence x⁽¹⁾ composed of the M numerical values to themultiplier 12 ₁. In the same way, the converter 11 ₂ also having aconfiguration identical with the converter 11 _(j) described aboveconverts the information-bit sequence b⁽²⁾ consisting of N₂ input bitsinto M numerical values located in the M-dimensional real-number vectorspace, and supplies an encoded sequence x⁽²⁾ composed of the M numericalvalues to the multiplier 12 ₂.

[0117] The multiplier 12 ₀ multiplies the encoded sequence x⁽⁰⁾ receivedfrom the converter 11 ₀ by constants a⁽⁰⁾ set by adoption of the methoddescribed above, and supplies a constant-times encoded sequence a⁽⁰⁾x⁽⁰⁾obtained as a result of the multiplication to the adder 13 ₀.

[0118] In the same way as the multipliers 12 ₀, the multiplier 12 ₁,multiplies the encoded sequence x⁽¹⁾received from the converter 11 ₁ byconstants a⁽¹⁾ set by adoption of the method described above, andsupplies a constant-times encoded sequence a⁽¹⁾x⁽¹⁾ obtained as a resultof the multiplication also to the adder 13 ₀.

[0119] In the same way as the multipliers 12 ₀ and 12 ₁, the multiplier12 ₂ multiplies the encoded sequence x⁽²⁾ received from the converter 11₂ by constants a⁽²⁾ set by adoption of the method described above, andsupplies a constant-times encoded sequence a⁽²⁾x⁽²⁾ obtained as a resultof the multiplication to the adder 13 ₁.

[0120] The adder 13 ₀ adds the constant-times encoded sequence a⁽⁰⁾x⁽⁰⁾received from the multiplier 12 ₀ to the constant-times encoded sequencea⁽¹⁾x⁽¹⁾ received from the multiplier 12 ₁, in an Euclid way for eachconstituent, and supplies an additive encoded sequence a⁽⁰⁾x⁽⁰⁾+a⁽¹⁾x⁽¹⁾obtained as a result of the addition to the adder 13 ₁.

[0121] The adder 13 ₁ adds the additive encoded sequencea⁽⁰⁾x⁽⁰⁾+a⁽¹⁾x⁽¹⁾ received from the adder 13 ₀ to the constant-timesencoded sequence a⁽²⁾x⁽²⁾ received from the multiplier 12 ₂ in an Euclidway for each constituent, and supplies a final additive encoded sequenceg(=a⁽⁰⁾x⁽⁰⁾+a⁽¹⁾x⁽¹⁾+a⁽²⁾x⁽²⁾) obtained as a result of the addition tothe transmission unit 14.

[0122] The transmission unit 14 is an interface for transmitting data tothe external component. To put it concretely, the transmission unit 14transmits the additive encoded sequence g received from the adder 131 tothe external component as a transmission signal g′.

[0123] When the transmission apparatus 10 described above receives 3information-bit sequences {b⁽⁰⁾, b⁽¹⁾, b⁽²⁾}, the transmission apparatus10 carries out a predetermined encoding process on the information-bitsequences {b⁽⁰⁾, b⁽¹⁾, b⁽²⁾} and, in order to transmit each of theinformation-bit sequences {b⁽⁰⁾, b⁽¹⁾, b⁽²⁾} by expending energy E_(b)[J] for achieving a desired bit error rate, the transmission apparatus10 multiplies encoded sequences {x⁽⁰⁾, x⁽¹⁾, x⁽²⁾}, which have beenobtained as a result of the encoding process, by constants {a⁽⁰⁾, a⁽¹⁾,a⁽²⁾} to result in constant-times encoded sequences {a⁽⁰⁾x⁽⁰⁾a⁽¹⁾x⁽¹⁾,a⁽²⁾x⁽²⁾}. Then, the transmission apparatus 10 sums up theconstant-times encoded sequences {a⁽⁰⁾x⁽⁰⁾, a⁽¹⁾x⁽¹⁾, a⁽²⁾ x⁽²⁾} toyield an additive encoded sequence g. The additive encoded sequence ggenerated by the transmission apparatus 10 is transmitted as atransmission signal to the reception apparatus through a communicationline, along which a noise n is added to the signal before the signalarrives at a reception apparatus to be described later.

[0124] The following description explains a reception apparatus employedin the data transmission and reception system. The reception apparatusreceives a reception signal y^((L)), which is a sum of the transmissionsignal transmitted by the transmission apparatus as a transmissionsignal and the noise n as shown in Eq. (35) given below. The receptionapparatus is capable of carrying out a decoding process to generate atleast one of the information-bit sequences b⁽¹⁾. To be more specific,when the reception apparatus receives the reception signal y^((L)), thereception apparatus is capable of carrying out a decoding process togenerate at least the information-bit sequence b^((L−1)) having thehighest order among the information-bit sequences b⁽¹⁾ encoded by thetransmission apparatus. The information-bit sequence b^((L−1)) is aninformation-bit sequence last added and transmitted by expending thegreatest information-bit energy E_(b). $\begin{matrix}\begin{matrix}{y^{(L)} = {{g\left( {b^{(0)},b^{(1)},\quad \ldots \quad,b^{({L - 1})}} \right)} + n}} \\{= {{\sum\limits_{l = 0}^{L - 1}{a^{(l)}{x^{(l)}\left( b^{(l)} \right)}}} + n}}\end{matrix} & (35)\end{matrix}$

[0125] In general, the reception apparatus has a typical configurationshown in FIG. 12. As shown in the figure, the reception apparatus 50 hasL decoders 51 _(L−1), 51 ^(L−2), . . . and 51 ₀, (L−1) converters 52_(L−1), 52 _(L−2), . . . and 52 ₁, (L−1) multipliers 53 _(L−2), 53_(L−2), . . . and 53 ₁ and (L−1) subtractors 54 _(L−1), 54 _(L−2), . . .and 54 ₁. The decoders 51 _(L−1), 5 _(L−2), . . . and 51 ₀ serve ascounterparts of the corresponding encoders employed in the transmissionapparatus. The converters 52 _(L−1), 52 _(L−2), . . . and 52 ₁ areidentical with the converters employed in the transmission apparatus.The multipliers 53 _(L−1), 53 _(L−2), . . . and 53 ₁ are identical withthe multipliers employed in the transmission apparatus.

[0126] First of all, the reception apparatus 50 carries out a decodingprocess to produce the information-bit sequence b^((L−1)). As describedearlier, the information-bit energy E_(b) ^((L−1)) is set at a value ξtimes the sum of the power density of the noise n and the powerdensities of the code x⁽⁰⁾ to the code x^((L−2)). Thus, the receptionapparatus 50 is capable of carrying out a decoding process to producedata with an error rate of 0 or an error rate having a value close to 0.Assume that the reception apparatus 50 is capable of accurately decodinga received value y^((L)) input by a reception unit, which is not shownin the figure, by using the decoder 51 _(L−1) to produce theinformation-bit sequence b^((L−1)). In this case, the information-bitsequence b^((L−1)) obtained as a result of the decoding process isre-encoded by the converter 52 _(L−1) to generate the encoded sequencex^((L−1)). The multiplier 53 _(L−1) then multiplies the encoded sequencex^((L−1)) by a constant a^((L−1)) to produce the constant-times encodedsequence a^((L−1))x^((L−1)). Then, the subtractor 54 _(L−1) subtractsthe constant-times encoded sequence a^((L−1))x^((L−1)) from the receivedvalue y^((L)) for each constituent. In this way, as shown in Eq. (36)given below, the reception apparatus 50 is capable of obtaininginformation y^((L−1)) equivalent to a value, which is received when acode obtained as a result of an encoding process carried out by thetransmission apparatus on information-bit sequences up to theinformation-bit sequence b^((L−2)) is received. $\begin{matrix}\begin{matrix}{y^{({L - 1})} = {y^{(L)} - {a^{({L - 1})}{x\left( b^{({L - 1})} \right)}}}} \\{= {{\sum\limits_{i = 0}^{L - 2}{a^{(l)}{x^{(l)}\left( b^{(l)} \right)}}} + n}}\end{matrix} & (36)\end{matrix}$

[0127] By the same token, assume that the reception apparatus 50 iscapable of accurately decoding a received value y^((L−1)) input by thereception unit by using the decoder 51 _(L−2) to produce theinformation-bit sequence b^((L−2)). In this case, the information-bitsequence b^((L−2)) obtained as a result of the decoding process isre-encoded by the converter 52 _(L−2) to generate the encoded sequencex^((L−2)). The multiplier 53 _(L−2) then multiplies the encoded sequencex^((L−2)) by a constant a^((L−2)) to produce the constant-times encodedsequence a^((L−2))x^((L−2)). Then, the subtractor 54 _(L−2) subtractsthe constant-times encoded sequence a^((L−2))x^((L−2)) from the receivedvalue y^((L−1)) for each constituent. In this way, as shown in Eq. (37)given below, the reception apparatus 50 is capable of obtaininginformation y^((L−2)) equivalent to a value, which is received when acode obtained as a result of an encoding process carried out by thetransmission apparatus on information-bit sequences up to theinformation-bit sequence b^((L−3)) is received. $\begin{matrix}\begin{matrix}{y^{({L - 2})} = {y^{({L - 1})} - {a^{({L - 2})}{x\left( b^{({L - 2})} \right)}}}} \\{= {{\sum\limits_{i = 0}^{L - 3}{a^{(l)}{x^{(l)}\left( b^{(l)} \right)}}} + n}}\end{matrix} & (37)\end{matrix}$

[0128] By carrying out the same operations repeatedly, the receptionapparatus 50 is capable of sequentially performing the decoding processto generate the information-bit sequences b⁽¹⁾. For the lastinformation-bit sequence b⁽⁰⁾, as shown in Eq. (38) given below, thereception apparatus 50 is capable of obtaining information y⁽¹⁾equivalent to a value, which is received when a code obtained as aresult of an encoding process carried out by the transmission apparatuson information-bit sequences up to the information-bit sequence b⁽⁰⁾ isreceived. That is to say, the reception apparatus 50 is capable ofcarrying out a decoding process to generate the information-bit sequenceb⁽⁰⁾.

y ⁽¹⁾ =x ⁽⁰⁾(b ⁽⁰⁾)+n  (38)

[0129] As described above, when a received value y^((L)) is input, thereceived value y^((L)) is decoded to produce the highest-orderinformation-bit sequence b^((L−1)). Then, the information-bit sequenceb^((L−1)) obtained as a result of the decoding process is re-encoded togenerate the encoded sequence x^((L−1)). The encoded sequence x^((L−1))is then multiplied by a constant a^((L−1)) to produce the constant-timesencoded sequence a^((L−1))x^((L−1)). Then, the constant-times encodedsequence a^((L−1))x^((L−1)) is subtracted from the received valuey^((L)). In this way, it is thus possible to carry out a decodingprocess to produce the next-order information-bit sequence b^((L−2)). Bycarrying out the same operations repeatedly for the information-bitsequences up to the last information-bit sequence b⁽⁰⁾ as describedabove, the reception apparatus 50 is capable of performing decodingprocesses to generate all the information-bit sequences {b⁽⁰⁾, b⁽¹⁾, . .. b^((L−1))}.

[0130] In addition, the reception apparatus 50 does not have to carryout all the decoding processes to generate all the information-bitsequences {b⁽⁰⁾, b⁽¹⁾, . . . , b^((L−1))}. Instead, the receptionapparatus 50 may carry out a decoding process to produce only thehighest-order information-bit sequence b^((L−1)). As an alternative, thereception apparatus 50 may also carry out some of decoding processes toproduce only information-bit sequences b⁽¹⁾ ranging from the highestorder to a predetermined order.

[0131] The data transmission and reception system described above iseffective for, among others, the case of an assumed application in whicha transmission apparatus encodes picture data having a variety ofresolutions and transmits the encoded picture data to a receptionapparatus 50 whereas the reception apparatus 50 decodes the encodedpicture data and displays the picture data. That is to say, thetransmission apparatus prepares the resolutions for picture data havingthe same contents. The transmission apparatus then encodes a pluralityof pieces of such picture data as the same plurality of information-bitsequences b⁽¹⁾. The transmission apparatus starts the encoding processwith an operation to encode the picture data having the highestresolution as an information-bit sequence of the lowest order, that is,the information-bit sequence b⁽⁰⁾. Then, the transmission apparatuscontinues the encoding process with operations to encode the pieces ofpicture data with lower resolutions in an order of decreasingresolutions as information-bit sequences with sequentially increasingorders. That is to say, the lower the resolution of picture data, themore the importance attached by the transmission apparatus to the dataand the larger the amplitude at which the data is transmitted.

[0132] On the other hand, when the reception apparatus 50 inputsreceived values y^((L)), the reception apparatus 50 decodes the receivedvalues y^((L)) sequentially to generate the information-bit sequencesb⁽¹⁾. As the decoding process to generate information-bit sequences b⁽¹⁾representing pieces of picture data, which correspond to the resolutionof a display unit employed in the reception apparatus 50, is completed,the decoding process is ended without decoding received values y^((L))to generate information-bit sequences of orders lower than the ordercorresponding to the resolution of the display unit. In this way, thereception apparatus 50 is capable of selectively carrying out decodingprocesses to generate only picture data that can be displayed on its owndisplay unit and displaying the picture data on the display unit.

[0133] As described above, the reception apparatus 50 does not carry outdecoding processes to generate all the information-bit sequences {b⁽⁰⁾,b⁽¹⁾, . . . , b^((L−1))}, but carries out only a decoding process togenerate the high-order information-bit sequence b^((L−1)) of muchimportance.

[0134] By the way, in the case of code satisfying Shannon's limit,errors are eliminated completely within a border defined by a certainsignal-to-noise power ratio E_(b)/n_(o). That is to say, it is knownthat, at signal-to-noise power ratios lower than this signal-to-noisepower ratio E_(b)/n_(o), errors are generated abruptly. In the case of atransmission through a communication line causing a signal-to-noisepower ratio lower even slightly than the signal-to-noise power ratioE_(b)/n_(o) required for entire code, the reception apparatus generatesa detrimental error in a first decoding process to produce thehighest-order information-bit sequence b^((L−1)), making it completelyimpossible to carry out subsequent decoding processes to generateinformation-bit sequences b^((L−2)), . . . , and b⁽⁰⁾each having anorder lower than the order of the highest-order information-bit sequenceb^((L−1)). In the case of a transmission through a communication linecausing a signal-to-noise power ratio higher even slightly than thesignal-to-noise power ratio E_(b)/n_(o) required for entire code, on theother hand, the reception apparatus is capable of carrying out decodingprocesses to generate all the information-bit sequences b⁽¹⁾ at an errorrate of 0.

[0135] In the present state of the contemporary actual code, however, itis impossible to obtain such an abrupt characteristic. Even in such acase, nevertheless, if the original code is code for which the so-calledMAP (Maximum A Posteriori) probability decoding process or a decodingprocess conforming to the MAP decoding process can be carried out, adecoding process can be performed to generate actual code with many orfew errors left.

[0136] Thus, in the data transmission and reception system, there hasbeen proposed a reception apparatus capable of carrying out the MAPdecoding process as an actual reception apparatus.

[0137] In the MAP decoding process, posteriori probability informationestimated from a received value for a candidate of a transmitted signalis found with the likelihood of the received value used as an input. Atransmission system of the data transmission and reception system isexpressed by Eq. (39) given below. When a decoding operation is carriedout in the MAP decoding process to generate the information-bit sequenceb^((i)), the likelihood of the information-bit sequence b^((i)) isexpressed by a conditional probability P(y^((L))|b^((i))) shown in Eq.(40) given below. $\begin{matrix}{y^{(L)} = {{{g\left( {b^{(0)},b^{(1)},\quad \ldots \quad,b^{({L - 1})}} \right)} + n} = {x + n}}} & (39) \\\begin{matrix}{{Likelihood}^{(i)} = {p\left( y^{(L)} \middle| b^{(i)} \right)}} \\{{\propto {\sum\limits_{\underset{i = 1}{b^{(i)}}}{{P\left( b^{(0)} \right)}{P\left( b^{(1)} \right)}{{\ldots P}\left( b^{({L - 1})} \right)}{\exp\left\lbrack {- \frac{1}{n_{0}}} \middle| {y^{(L)} -} \right.}}}}} \\\left. {g\left( {b^{(0)},b^{(1)},\quad \ldots \quad,b^{({L - 1})}} \right)}^{2} \right\rbrack\end{matrix} & (40)\end{matrix}$

[0138] Symbol Σ in Eq. (40) is an operator for finding a sum forcandidates of all information-bit sequences b⁽¹⁾ with respect to allvalues of 1 except i. Symbol P(b^((j))) in Eq. (40) denotes aprobability at which the information-bit sequence b^((j)) is generated.It should be noted that, at the stage of starting the decoding process,it is impossible to identify which code is received. Thus, the initialvalue of the probability P(b^((j))) is expressed by Eq. (41) as follows:

P(b ⁽¹⁾)=½^(N)  (41)

[0139] The reception apparatus carries out decoding processes, startingwith a decoding process to generate a high-order information-bitsequence. Thus, posteriori probability information obtained as a resultof a MAP decoding process can be used in finding a next decodinglikelihood value. For this reason, even if many or few uncertain errorsare left in a result of a decoding process, it is possible to carry outa decoding process adding the errors in the decoding process at the nextstage. In this case, in the reception apparatus, a bad effect of thedecoding process carried out at the preceding stage is inherited by thedecoding process at the next stage. Since the deterioration of thecharacteristic is not that bad, however, there is no detrimental effect.

[0140] By decomposing all the sequences' likelihood expressed by Eq.(40) given before into pieces of likelihood for M dimensional elements,the likelihood can be expressed by Eq. (42) as follows. $\begin{matrix}{{Likelihood}^{(i)} = {p\left( {{y^{(L)}\left. b^{(i)} \right)} = {p\left( {{y^{(L)}\left. {x\left( b^{(i)} \right)} \right)} = {\prod\limits_{k = 0}^{M - 1}\quad {p\left( {{y_{k}^{(L)}\left. x_{k}^{(i)} \right)} \propto {\prod\limits_{k = 0}^{M - 1}{\sum\limits_{\underset{l = i}{x_{i}^{(1)}}}^{\quad}{{P\left( x_{t}^{(0)} \right)}{P\left( x_{k}^{(i)} \right)}\quad \ldots \quad {P\left( x_{k}^{({L - 1})} \right)}{\exp \left\lbrack {{- \frac{1}{n_{0}}}{{y_{k}^{(L)} - {\sum\limits_{j = 0}^{L - 1}{a^{(j)}x_{k}^{(j)}}}}}^{2}} \right\rbrack}}}}} \right.}}} \right.}} \right.}} & (42)\end{matrix}$

[0141] Symbol P(x_(k) ⁽¹⁾) in Eq. (42) is a probability at which the kthcomponent of an M-dimensional vector of a code word for theinformation-bit sequence b^((j)) is x_(k) ⁽¹⁾. Symbol Σ in Eq. (42) isan operator for finding a sum for all possible components x_(k) ⁽¹⁾ withrespect to all values of 1 except i. It should be noted that, if adecoding process can be carried out at the preceding stage withoutleaving ambiguity at all, the probability P(x_(k) ^((j))) for a specificcomponent x_(k) ^((j)) is equal to 1. Thus, this processing is equal tocancellation by carrying out a re-encoding process.

[0142] As described above, if the MAP decoding process is applicable tothe original signal, the reception apparatus is capable of carrying outa decoding process to produce all the information-bit sequences {b⁽⁰⁾,b⁽¹⁾, . . . , b^((L−1))} by reflecting a result of a MAP decodingprocess carried out to generate an information-bit sequence b⁽¹⁾ inprocessing to find a likelihood value for another information-bitsequence.

[0143] It should be noted that, in the case of a transmission through adynamic communication line called a Rayleigh fading channel, thesignal-to-noise power ratio E_(b)/n_(o) required by the original signaldeteriorates slightly in comparison with the AWGN channel. In this case,the transmission apparatus needs to construct code by assuming arequired signal-to-noise power ratio of E_(b)/(n_(o)+2ν), which is foundfor a communication line to be used for the transmission. Since thenoise source for high-order code is a source generating a thermal noise,which is a kind of low-order code, as described above, however, thelevel of low-order code varies along with the high-order code. For thisreason, the deviation of variations in high-order code becomes smaller,setting the required signal-to-noise power ratio E_(b)/(n_(o)+2ν) in adecreasing trend as well. As a result, the required signal-to-noisepower ratio E_(b)/(n_(o)+2ν) for all codes is expected to decrease lessthan a deterioration of the signal-to-noise power ratio ofE_(b)/(n_(o)+2ν) for a single code. Here, let the amplitude f on thedynamic communication line be expressed by Eq. (43) given below. In thiscase, the received value y is expressed by Eq. (44) given below.Accordingly, the likelihood is expressed by Eq. (45) as follows.

f={f₀,f₁, . . . , f_(N−1)}^(T)  (44)

y=f ^(T) ·g+n  (44) $\begin{matrix}\begin{matrix}{{Likelihood}^{(i)} = {p\left( {y^{(L)}{b^{(i)}}} \right)}} \\{= {p\left( {y^{(L)}{{x\left( b^{(i)} \right)}}} \right)}} \\{= {\prod\limits_{k = 0}^{M - 1}\quad {p\left( {{y_{k}^{(L)}\left. x_{k}^{(i)} \right)} \propto {\prod\limits_{k = 0}^{M - 1}{\sum\limits_{\underset{l = i}{x_{i}^{(1)}}}^{\quad}{{P\left( x_{k}^{(0)} \right)}{P\left( x_{k}^{(1)} \right)}\quad \ldots}}}}\quad \right.}}} \\{{P\left( x_{k}^{({L - 1})} \right){\exp \left\lbrack {{- \frac{1}{n_{0}}}{{y_{k}^{(L)} - {f_{k} \cdot {\sum\limits_{j = 0}^{L - 1}{a^{(j)}x_{k}^{(j)}}}}}}^{2}} \right\rbrack}}}\end{matrix} & (45)\end{matrix}$

[0144] Now, the following description explains a concrete configurationof the reception apparatus, which is used for carrying out such adecoding process, in detail. It should be noted that, in order to makethe following explanation easy to describe, the reception apparatus isan apparatus for receiving a reception signal y′ comprising the receivedvalue y, which is the sum of a noise n and a transmission signal g′encoded and transmitted by the transmission apparatus 10 describedabove. That is to say, the reception apparatus is an apparatus forcarrying out decoding processes to obtain soft-decision values of theinformation-bit sequences {b⁽⁰⁾b⁽¹⁾, b⁽²⁾}.

[0145] As shown in FIG. 13, the reception apparatus 60 typicallycomprises a reception unit 61 for receiving a reception signal y′transmitted by an external apparatus and 3 decoders 62 ₀, 62 ₁ and 62 ₂each used for carrying out a turbo decoding process corresponding to thePCCC-encoding process performed by the converters 11 ₀, 11 ₁ and 11 ₂employed in the transmission apparatus 10 described above.

[0146] The reception unit 61 is an interface for receiving data from anexternal apparatus. When the reception unit 61 receives a receptionsignal y′, the reception unit 61 supplies the reception signal y′ todecoders 62 ₀, 62 ₁ and 62 ₂ as a received value y.

[0147] The decoders 62 ₀, 62 ₁ and 62 ₂ are provided as counterparts ofrespectively the converters 11 ₀, 11 ₁ and 11 ₂ employed in thetransmission apparatus 10. The decoders 62 ₀, 62 ₁ and 62 ₂ includerespectively likelihood computation units 63 ₀, 63 ₁ and 63 ₂ forfinding a likelihood value of a reception symbol from the received valuey. The decoders 62 ₀, 62 ₁ and 62 ₂ each find posteriori probabilityinformation for an information bit by carrying out a turbo decodingprocess corresponding to the PCCC-encoding process performed by theconverters 11 ₀, 11 ₁ and 11 ₂ employed in the transmission apparatus10. The decoders 62 ₀, 62 ₁ and 62 ₂ will be described in detail later.

[0148] The reception apparatus 60 described above is characterized inthat the decoders 62 ₀, 62 ₁ and 62 ₂ output pieces of posterioriprobability information P(x⁽⁰⁾|y), P(x⁽¹⁾|y) and P(x⁽²⁾|y) for encodedsequences {x⁽⁰⁾, x⁽¹⁾, x⁽²⁾} generated by the decoders 62 ₀, 62 ₁ and 62₂ respectively. To put it in detail, the reception apparatus 60described above is characterized in that the decoder 62 ₀ outputs theposteriori probability information P(x⁽⁰⁾|y) as priori probabilityinformation P(x⁽⁰⁾) for the encoded sequence x⁽⁰⁾ to the other decoders62 ₁ and 62 ₂. In addition, the reception apparatus 60 described aboveis also characterized in that the decoder 62 ₁ outputs the posterioriprobability information P(x⁽¹⁾|y) as priori probability informationP(x⁽¹⁾) for the encoded sequence x⁽¹⁾ to the other decoders 62 ₀ and 62₂. Furthermore, the reception apparatus 60 described above is furthercharacterized in that the decoder 62 ₂ outputs the posterioriprobability information P(x⁽²⁾|y) as priori probability informationP(x⁽²⁾) for the encoded sequence x⁽²⁾ to the other decoders 62 ₀ and 62₁. In an initial state, an initial value of the priori probabilityinformation P(x⁽¹⁾) and an initial value of the priori probabilityinformation P(x⁽²⁾) are supplied to the decoder 62 ₀. In addition, aninitial value of the priori probability information P(x⁽⁰⁾) and aninitial value of the priori probability information P(x⁽²⁾) are suppliedto the decoder 62 ₁. Furthermore, an initial value of the prioriprobability information P(x⁽⁰⁾) and an initial value of the prioriprobability information P(x⁽¹⁾) are supplied to the decoder 62 ₂. Theinitial values each represent an unknown probability. In this case,since each constituent of the encoded sequences {x⁽⁰⁾, x⁽¹⁾,x⁽²⁾} hasbeen subjected to a signal-point mapping process based on the BPSKmodulation method in the transmission apparatus 10,P(x⁽¹⁾=1|y)=P(x⁽¹⁾=1)=0.5 and P(x⁽¹⁾=−1|y)=P(x⁽¹⁾=−1)=0.5.

[0149] When the reception apparatus 60 receives a received value y,first of all, the reception apparatus 60 supplies the received value yto the decoder 62 ₂. In addition, the decoder 62 ₂ employed in thereception apparatus 60 also receives the priori probability informationP(x⁽⁰⁾) for the encoded sequence x⁽⁰⁾ and the priori probabilityinformation P(x⁽¹⁾) for the encoded sequence x⁽¹⁾ The decoder 62 ₂employed in the reception apparatus 60 carries out a turbo decodingprocess on the received value y, the priori probability informationP(x⁽⁰⁾) and the priori probability information P(x⁽¹⁾) to generate theposteriori probability information P(x⁽²⁾|y) for the encoded sequencex⁽²⁾ and the posteriori probability information P(b⁽²⁾|y) for theinformation-bit sequence b⁽²⁾. Then, the decoder 622 employed in thereception apparatus 60 supplies the posteriori probability informationP(x⁽²⁾|y) to the decoders 62 ₀ and 62 ₁ as the priori probabilityinformation P(x⁽²⁾) for the encoded sequence x⁽²⁾, and supplies theposteriori probability information P(b⁽²⁾|y) to an external component asa soft-output.

[0150] Subsequently, the reception unit employed in the receptionapparatus 60 supplies the received value y to the decoder 62 ₁ afterdelaying the received value y by a delay time equal in length to theprocessing time of the decoder 62 ₂. In addition, the decoder 62 ₁employed in the reception apparatus 60 also receives the prioriprobability information P(x⁽⁰⁾) for the encoded sequence x⁽⁰⁾ and thepriori probability information P(x⁽²⁾) for the encoded sequence x⁽²⁾.The decoder 62 ₁ employed in the reception apparatus 60 carries out aturbo decoding process on the received value y, the priori probabilityinformation P(x⁽⁰⁾) and the priori probability information P(x⁽²⁾) togenerate the posteriori probability information P(x⁽¹⁾|y) for theencoded sequence x⁽¹⁾ and the posteriori probability informationP(b⁽¹⁾|y) for the information-bit sequence b⁽¹⁾. Then, the decoder 62 ₁employed in the reception apparatus 60 supplies the posterioriprobability information P(x⁽¹⁾|y) to the decoder 62 ₀ and, if necessary,the decoder 62 ₂ as the priori probability information P(x⁽¹⁾) for theencoded sequence x⁽¹⁾, and supplies the posteriori probabilityinformation P(b⁽¹⁾|y) to the external component as a soft-output.

[0151] Subsequently, the reception unit employed in the receptionapparatus 60 supplies the received value y to the decoder 62 ₀ afterdelaying the received value y by a delay time equal in length to the sumof the processing time of the decoder 62 ₁ and the processing time ofthe decoder 62 ₂. In addition, the decoder 62 ₀ employed in thereception apparatus 60 also receives the priori probability informationP(x⁽¹⁾) for the encoded sequence x⁽¹⁾ and the priori probabilityinformation P(x⁽²⁾) for the encoded sequence x⁽²⁾ The decoder 62 ₀employed in the reception apparatus 60 carries out a turbo decodingprocess on the received value y, the priori probability informationP(x⁽¹⁾) and the priori probability information P(x⁽²⁾) to generate theposteriori probability information P(x⁽⁰⁾|y) for the encoded sequencex⁽⁰⁾ and the posteriori probability information P(b⁽⁰⁾|y) for theinformation-bit sequence b⁽⁰⁾. Then, the decoder 62 ₀ employed in thereception apparatus 60 supplies the posteriori probability informationP(x⁽⁰⁾|y) to the decoders 62 ₁ and 62 ₂ if necessary as the prioriprobability information P(x⁽⁰⁾) for the encoded sequence x⁽⁰⁾, andsupplies the posteriori probability information P(b⁽⁰⁾|y) to theexternal component as a soft-output.

[0152] By carrying out the operations described above, the receptionapparatus 60 is capable of carrying out decoding processes to generatethe pieces of posteriori probability information P(b⁽²⁾|y), P(b⁽¹⁾|y)and P(b⁽⁰⁾|y) in an enumeration order of P(b⁽²⁾|y), P(b⁽¹⁾|y) andP(b⁽⁰⁾|y). In the reception apparatus 60, a hard-decision unit not shownin the figure converts the pieces of posteriori probability informationP(b⁽²⁾|y), P(b⁽¹⁾|y) and P(b⁽⁰⁾|y) into binary values to obtain theinformation-bit sequences b⁽²⁾, b⁽¹⁾ and b⁽⁰⁾. It should be noted that,while the reception apparatus 60 carries out a decoding process onlyonce sequentially to generate information-bit sequences starting withthe information-bit sequence b⁽²⁾, the reception apparatus 60 is alsocapable of performing the so-called zigzag decoding process or theso-called repetitive decoding process as will be described later.

[0153] The following description explains the decoders 62 ₀, 62 ₁ and 62₂ for carrying out the turbo decoding process. First of all, an ordinaryturbo decoder for carrying out a turbo decoding process of one encodedsequence is explained to clarify the characteristic of the decoders 62₀, 62 ₁ and 62 ₂ applied to the reception apparatus 60. It should benoted that, in this case, in order to make the following explanationeasy to describe, a turbo decoder serving as the counterpart of theconverter 11 _(j) shown in FIG. 10 is explained first.

[0154] As shown in FIG. 14, an ordinary turbo decoder 70 comprises achannel de-interleaver 71, a de-puncture unit 72, 2 interleavers 73 and75, 2 MAP decoders 74 and 76 and a de-interleaver 77. The channelde-interleaver 71 used for a channel restores pieces of input data to anoriginal order. The de-puncture unit 72 restores discretely reduced datato the original data. The interleavers 73 and 75 each rearrange theorder of pieces of input data. The MAP decoders 74 and 76 each carry outa MAP decoding process. The de-interleaver 77 restores pieces of inputdata to the original order.

[0155] The channel de-interleaver 71 is provided if the converter 11_(j) described earlier includes the channel interleaver 24. The channelde-interleaver 71 inputs the received value y and de-interleaves thereceived value y to restore the bit array of the interleaved data De tothe bit array of the original information-bit sequence b^((i)) and thebit array of the original puncture data Dd. The interleaved data De hasbeen interleaved by the channel interleaver 24 employed in the converter11 _(j). A sequence Df is the de-interleaving process' resultcorresponding to the information-bit sequence b^((i)). On the otherhand, a sequence Dg is the de-interleaving process' result correspondingto the puncture data Dd. The channel de-interleaver 71 supplies thesequence Df to the interleaver 73 and the MAP decoder 74 but suppliesthe sequence Dg to the de-puncture unit 72.

[0156] The de-puncture unit 72 restores the sequence Dg received fromthe channel de-interleaver 71 by inserting data such as 0.0 intopositions of bits discretely reduced by the puncture unit 23 employed inthe converter 11 _(j) to generate 2 sequences Dh and Di corresponding torespectively the 2 sequences Da and Dc output by the element encoders 21₀ and 21 ₁ respectively. The de-puncture unit 72 supplies the sequenceDh to the MAP decoder 74 and the sequence Di to the MAP decoder 76.

[0157] The interleaver 73 inputs the sequence Df supplied by the channelde-interleaver 71, and interleaves the sequence Df on the basis of thesame information on permutation locations as the interleaver 22 employedin the converter 11 _(j). The interleaver 73 then supplies a sequence Djobtained as a result of the interleaving process to the MAP decoder 76.

[0158] The MAP decoder 74 is provided as a counterpart of the elementencoder 21 ₀ employed in the converter 11 _(j). The MAP decoder 74receives the soft-input sequence Df corresponding to the information-bitsequence b^((i)) from the channel de-interleaver 71, the soft-inputsequence Dh from the de-puncture unit 72 and priori probabilityinformation Apr₀ for a soft-input information bit from thede-interleaver 77. The MAP decoder 74 then carries out a MAP decodingprocess on the sequence Df, the sequence Dh and the priori probabilityinformation Apr₀. Then, the MAP decoder 74 generates the so-calledextrinsic information Ext₀ for an information-bit sequence to be foundby using a code constraint condition and supplies this extrinsicinformation Ext₀ to the interleaver 75 as a soft-output. It should benoted that the extrinsic information Ext₀ represents an increase inlikelihood.

[0159] The interleaver 75 interleaves the extrinsic information Ext₀received from the MAP decoder 74 as a soft input corresponding to aninformation-bit sequence on the basis of the same information onpermutation locations as the interleaver 22 employed in the converter 11_(j). The interleaver 75 then supplies priori probability informationApr₁ for an information bit in the MAP decoder 76 as a result of theinterleaving process to the MAP decoder 76.

[0160] The MAP decoder 76 is provided as a counterpart of the elementencoder 21 ₁ employed in the converter 11 _(j). The MAP decoder 76receives the soft-input sequence Dj corresponding to the information-bitsequence b^((i)) from the channel interleaver 73, the soft-inputsequence Di from the de-puncture unit 72 and the priori probabilityinformation Apr₁ for soft-input information bits from the interleaver75. The MAP decoder 76 then carries out a MAP decoding process on thesequence Dj, the sequence Di and the priori probability informationApr₁. Then, the MAP decoder 76 generates the so-called extrinsicinformation Ext1 for an information-bit sequence to be found by using acode constraint condition and supplies this extrinsic information Ext₁to the de-interleaver 77 as a soft-output. It should be noted that, muchlike the extrinsic information Ext₀, the extrinsic information Ext₁represents an increase in likelihood. In addition, the MAP decoder 76generates posteriori probability information P(b|y) for an informationbit on the basis of soft-output external information obtained as aresult of a repetitive decoding process carried out repeatedly apredetermined plurality of times, and outputs the posteriori probabilityinformation P(b|y) as decoded data.

[0161] The de-interleaver 77 de-interleaves the extrinsic informationExt₁ received from the MAP decoder 76 as a soft input so as to restorethe bit array of the data Db interleaved by the interleaver 22 employedin the converter 11 _(j) to the bit array of the originalinformation-bit sequence b^((i)). The de-interleaver 77 then suppliesthe priori probability information Apr₀ for an information bit in theMAP decoder 74 as a result of the interleaving process to the MAPdecoder 74.

[0162] In the turbo decoder 70 described above, the MAP decoders 74 and76 find posteriori probability information Apo(b_(j)) by using thesoft-input sequences corresponding to the information-bit sequenceb^((i)) and the puncture data Dd and by using the pieces of prioriprobability information Apr₀ and Apr₁. The posteriori probabilityinformation Apo(b_(j)) is a probability at which an information bit at atime j is b_(j). To be more specific, the MAP decoders 74 and 76 findthe posteriori probability information Apo(b_(j)) in accordance with Eq.(46) as follows: $\begin{matrix}\begin{matrix}{{{Apo}\left( b_{j} \right)} = {P\left( {b_{j}{y}} \right)}} \\{= {{\sum\limits_{o \in C}^{\quad}{P\left( {b_{i},\left. b \middle| y \right.} \right)}} = {\sum\limits_{o \in C}^{\quad}\frac{{p\left( {\left. y \middle| b_{j} \right.,b} \right)}{P\left( {b_{j},b} \right)}}{p(y)}}}} \\{{\propto {\sum\limits_{o \in C}^{\quad}{{p\left( {\left. y \middle| b_{j} \right.,b} \right)}{P\left( {b_{j},b} \right)}}}} = {\sum\limits_{o \in {C\quad \beta_{i}}}^{\quad}{{p\left( y \middle| b \right)}{P(b)}}}} \\{= {{\sum\limits_{o \in {C\quad P_{j}}}^{\quad}{{p\left( y \middle| x \right)}{P(b)}}} = {\sum\limits_{o \in {C\quad P_{j}}}^{\quad}{\prod\limits_{k = 0}^{N - 1}\quad {{p\left( y_{k} \middle| x_{k} \right)}{P\left( b_{k} \right)}}}}}} \\{= {\sum\limits_{o \in {CP}_{j}}^{\quad}{\prod\limits_{k = 0}^{N - 1}\quad {{p\left( y_{k} \middle| x_{k} \right)}{{Apr}\left( b_{k} \right)}}}}}\end{matrix} & (46)\end{matrix}$

[0163] It should be noted that priori probability information Apr(b_(k))in Eq. (46) given above is defined by Eq. (47) as follows.

Apr(b _(k))=P(b _(k))  (47)

[0164] Since a code x is generated univocally by an encoding processrepresented by an equation x=x(b) if an information bit b is determined,Eq. (46) given above is transformed as shown by the second and thirdlines. Symbol Σ in Eq. (46) denotes summation taken with respect to allsequences for which c={c₀, c₁, . . . , C_(N−1)} is a code word and aninformation bit at a time j is b_(j).

[0165] Since the fifth line of Eq. (46) is merely proportional to theposteriori probability information Apo(b_(j)) as shown in Eq. (48) givenbelow, it is necessary to eventually normalize the posterioriprobability information Apo(b_(j)) as shown in Eq. (49) as follows.$\begin{matrix}{{{Apo}\left( b_{j} \right)} \propto {\sum\limits_{o \in {C\quad P_{j}}}^{\quad}{\prod\limits_{k = 0}^{N - 1}\quad {{p\left( y_{k} \middle| x_{k} \right)}{{Apr}\left( b_{k} \right)}}}}} & (48) \\{{\sum\limits_{b_{i}}^{\quad}{{Apo}\left( b_{j} \right)}} = 1} & (49)\end{matrix}$

[0166] As described above, the MAP decoders 74 and 76 are capable offinding the posteriori probability information Apo(b_(j)) by using thepriori probability information Apr(b_(k)) (=P(b_(k))) and the likelihoodL(=p(y_(k)|x_(k)) of a reception symbol for a candidate for atransmission symbol. It should be noted that, if the communication lineis an AWGN channel, for example, the likelihood L can be found by usingEq. (51) given below provided that the probability density function ofthe noise can be expressed by Eq. (50) as follows. $\begin{matrix}{{p_{n}(n)} = {\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp \left\lbrack {\frac{1}{2\sigma_{n}^{2}}{n}^{2}} \right\rbrack}}} & (50) \\{L = {{p\left( y_{k} \middle| x_{k} \right)} \propto {\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp \left\lbrack {\frac{1}{2\sigma_{n}^{2}}{{y_{k} - x_{k}}}^{2}} \right\rbrack}}}} & (51)\end{matrix}$

[0167] In the turbo decoder 70, the MAP decoder 74 outputs thedifference between the posteriori probability information Apo(b_(j)) andthe priori probability information Apr₀ as the external information Ext₀while the MAP decoder 76 outputs the difference between the posterioriprobability information Apo(b_(j)) and the priori probabilityinformation Apr₁ as the external information Ext₁.

[0168] When receiving the received value y, the turbo decoder 70comprising the MAP decoders 74 and 76 described above carries out arepetitive decoding process repeatedly a predetermined plurality oftimes. The MAP decoder 76 then generates posteriori probabilityinformation P(b|y) for an information bit on the basis of thesoft-output external information obtained as a result of this repetitivedecoding process, and outputs the posteriori probability informationP(b|y) as decoded data.

[0169] By the way, as described earlier, the reception apparatus 60 isprovided with the decoders 62 ₀, 62 ₁ and 62 ₂ each serving as animprovement of the turbo decoder 70 described above. It should be notedthat, in this case, in order to make the following explanation easy todescribe, the decoder 62 ₀ for carrying out a turbo decoding process inits capacity as a counterpart of the converter 11 _(j) shown in FIG. 10is explained first.

[0170] As shown in FIG. 15, the decoder 62 ₀ comprises a channelde-interleaver 81, a de-puncture unit 82, 2 interleavers 83 and 85, 2MAP decoders 84 and 86, a de-interleaver 87, a puncture unit 88 and achannel interleaver 88. The channel de-interleaver 81 used for a channelrestores pieces of input data to an original order. The de-puncture unit82 restores discretely reduced data to the original data. Theinterleavers 83 and 85 each rearrange the order of pieces of input data.The MAP decoders 84 and 86 each carry out a MAP decoding process. Thede-interleaver 87 restores pieces of input data to the original order.The puncture unit 88 carries out a proper discrete reduction process oninput data. The channel interleaver 89 used for a channel rearranges theorder of pieces of input data.

[0171] Much like the channel de-interleaver 71 employed in the turbodecoder 70 described above, the channel de-interleaver 81 is providedwhen the converter 11 _(j) described earlier includes the channelinterleaver 24. The channel de-interleaver 81 inputs the received valuey, priori probability information P(x⁽¹⁾) for an encoded sequence x⁽¹⁾and priori probability information P(x⁽²⁾) for an encoded sequence x⁽²⁾.The channel de-interleaver 81 then de-interleaves the received value y,the priori probability information P(x⁽¹⁾) and the priori probabilityinformation P(x⁽²⁾) to restore the bit array of the interleaved data Deto the bit array of the original information-bit sequence b^((i)) andthe bit array of the original puncture data Dd. The interleaved data Dehas been interleaved by the channel interleaver 24 employed in theconverter 11 _(j). Sequences Dk_(y), Dk₁ and Dk₂ are the de-interleavingprocess' results for respectively the information-bit sequence b^((i)),the priori probability information P(x⁽¹⁾) and the priori probabilityinformation P(x⁽²⁾), which correspond to the information-bit sequenceb⁽¹⁾. On the other hand, sequences Dl_(y), Dl₁ and Dl₂ are thede-interleaving process' results for respectively the information-bitsequence b^((i)), the priori probability information P(x⁽¹⁾) and thepriori probability information P(x⁽²⁾), which correspond to the puncturedata Dd. The channel de-interleaver 81 supplies the sequences Dk_(y),Dk₁ and Dk₂ to the interleaver 83 and the MAP decoder 84, but suppliesthe sequences Dl_(y), Dl₁ and Dl₂ to the de-puncture unit 82.

[0172] Much like the de-puncture unit 72 employed in the turbo decoder70 described above, the de-puncture unit 82 restores the sequence Dl_(y)received from the channel de-interleaver 81 by inserting data such as0.0 into positions of bits discretely reduced by the puncture unit 23employed in the converter 11 _(j) to generate a sequence Dm_(y) for thereceived value y corresponding to the output data Da output by theelement encoder 21 ₀ and generate a sequence Dn_(y) for the receivedvalue y corresponding to the output data Dc output by the elementencoder 21 ₁. In addition, the de-puncture unit 82 restores thesequences Dl₁ and Dl₂ received from the channel de-interleaver 81 byinserting data P(x⁽¹⁾=1)=0.5 and P(x⁽¹⁾=−1)=0.5 into positions of bitsdiscretely reduced by the puncture unit 23 employed in the converter 11_(j) to generate sequences Dm₁, Dm₂, Dn₁, and Dn₂. The 2 sequences Dm₁and Dm₂ generated for the priori probability information P(x⁽¹⁾) and thepriori probability information P(x⁽²⁾) respectively correspond to theoutput data Da output by the element encoder 21 ₀. On the other hand,the 2 sequences Dm₁ and Dm₂ generated for the priori probabilityinformation P(x⁽¹⁾) and the priori probability information P(x⁽²⁾)respectively correspond to the output data Dc output by the elementencoder 21 ₁. The de-puncture unit 82 then outputs the sequences Dm_(y),Dm₁ and Dm₂ generated thereby to the MAP decoder 84 but outputs thesequences Dn_(y), Dn₁ and Dn₂ generated thereby to the MAP decoder 86.

[0173] Much like the interleaver 73 employed in the turbo decoder 70described above, the interleaver 83 inputs the sequences Dk_(y), Dk₁ andDk₂ supplied by the channel de-interleaver 81, and interleaves thesequences Dk_(y), Dk₁ and Dk₂ on the basis of the same information onpermutation locations as the interleaver 22 employed in the converter 11_(j). The interleaver 83 then supplies sequences Do_(y), Do₁ and Do₂obtained as a result of the interleaving process to the MAP decoder 86.

[0174] Much like the MAP decoder 74 employed in the turbo decoder 70described above, the MAP decoder 84 is provided as a counterpart of theelement encoder 21 ₀ employed in the converter 11 _(j). The MAP decoder84 receives the soft-input sequences Dk_(y), Dk₁ and Dk₂ correspondingto the information-bit sequence b⁽¹⁾ from the channel de-interleaver 81,the soft-input sequences Dm_(y), Dm₁ and Dm₂ from the de-puncture unit82 and priori probability information Apr₀ for a soft-input informationbit from the de-interleaver 87. The MAP decoder 84 then carries out aMAP decoding process on the sequences Dk_(y), Dk₁, Dk₂, Dm_(y), Dm₁ andDm₂ as well as the priori probability information Apr₀. Then, the MAPdecoder 84 generates extrinsic information Ext₀ for an information-bitsequence to be found by using a code constraint condition and suppliesthis extrinsic information Ext₀ to the interleaver 85 as a soft-output.In addition, on the basis of soft-output external information generatedas a result of a repetitive decoding process carried out a predeterminedplurality of times, the MAP decoder 84 also generates posterioriprobability information Apo_(0i) for a soft-input information bit andposteriori probability information Apo_(0c) for an encoded bitcorresponding to the output data Da output by the element encoder 21 ₀employed in the converter 11 _(j). The MAP decoder 84 then outputs theposteriori probability information Apo_(0i) and the posterioriprobability information Apo_(0c) to the channel interleaver 89 and thepuncture unit 88 respectively. It should be noted that, much like theMAP decoder 74 employed in the turbo decoder 70 described above, the MAPdecoder 84 also finds a likelihood L except that the MAP decoder 84finds a likelihood L by carrying out a process different from the MAPdecoder 74. More information on this will be described later.

[0175] Much like the interleaver 75 employed in the turbo decoder 70described above, the interleaver 85 interleaves the extrinsicinformation Ext₀ received from the MAP decoder 84 as a soft inputcorresponding to an information-bit sequence on the basis of the sameinformation on permutation locations as the interleaver 22 employed inthe converter 11 _(j). The interleaver 85 then supplies prioriprobability information Apr₁ for an information bit in the MAP decoder86 as a result of the interleaving process to the MAP decoder 86.

[0176] Much like the MAP decoder 76 employed in the turbo decoder 70described above, the MAP decoder 86 is provided as a counterpart of theelement encoder 21 ₁ employed in the converter 11 _(j). The MAP decoder86 receives the soft-input sequences Do_(y), Do₁ and Do₂ correspondingto the information-bit sequence b^((i)) from the channel the inverter83, the soft-input sequences Dn_(y), Dn₁ and Dn₂ from the de-punctureunit 82 and the priori probability information Apr₁ for a soft-inputinformation bit from the interleaver 85. The MAP decoder 84 then carriesout a MAP decoding process on the sequences Do_(y), Do₁, Do₂, Dn_(y),Dn₁ and Dn₂ as well as the priori probability information Apr₁. Then,the MAP decoder 84 generates extrinsic information Ext₁ for aninformation bit to be found by using a code constraint condition andsupplies this extrinsic information Ext₁ to the de-interleaver 87 as asoft-output. Furthermore, the MAP decoder 86 generates posterioriprobability information P (b⁽⁰⁾|y) for an information bit sequence b⁽⁰⁾on the basis of soft-output external information obtained as a result ofa repetitive decoding process carried out repeatedly a predeterminedplurality of times, and outputs the posteriori probability informationP(b⁽⁰⁾|y) to an external component as decoded data. In addition, on thebasis of soft-output external information generated as a result of arepetitive decoding process carried out a predetermined plurality oftimes, the MAP decoder 86 also generates posteriori probabilityinformation Apo_(1c) for an encoded bit corresponding to the data Dcoutput by the element encoder 21 ₁ employed in the converter 11 _(j).The MAP decoder 86 then outputs the posteriori probability informationApo_(1c) to the puncture unit 88. It should be noted that, much like theMAP decoder 76 employed in the turbo decoder 70 described above, the MAPdecoder 86 also finds a likelihood L except that the MAP decoder 86finds a likelihood L by carrying out a process different from the MAPdecoder 76. More information on this will be described later.

[0177] Much like the interleaver 77 employed in the turbo decoder 70described above, the de-interleaver 87 de-interleaves the extrinsicinformation Ext₁ received from the MAP decoder 86 as a soft input so asto restore the bit array of the interleaved data Db interleaved by theinterleaver 22 employed in the converter 11 _(j) to the bit array of theoriginal information-bit sequence b^((i)). The de-interleaver 87 thensupplies the priori probability information Apr₀ for an information bitin the MAP decoder 84 as a result of the interleaving process to the MAPdecoder 84.

[0178] The puncture unit 88 receives the posteriori probabilityinformation Apo_(0c) for an encoded bit from the MAP decoder 84 and theposteriori probability information Apo_(1c) for an encoded bit from theMAP decoder 86, carrying out a discrete reduction process on theposteriori probability information Apo_(0c) and the posterioriprobability information Apo_(1c) on the basis of the same rule as thepuncture unit 23 employed in the converter 11 _(j). As a result of thediscrete reduction process, the puncture unit 88 then outputs puncturedata Dp with some bits thereof eliminated to the channel interleaver 89.

[0179] The channel interleaver 89 receives the puncture data Dp from thepuncture unit 88 and the posteriori probability information Apo_(0i)from the MAP decoder 84 with a timing delayed by a delay time equal inlength to the processing time of the puncture unit 88, rearranging theorder of bits composing the puncture data Dp and the posterioriprobability information Apo_(0i) on the basis of the same information onpermutation locations as the channel interleaver 24 employed in theconverter 11 _(j) to generate priori probability information P(x⁽⁰⁾|y)for the encoded sequence x⁽⁰⁾. The channel interleaver 89 finallyoutputs the priori probability information P(x⁽⁰⁾|y) to an externalcomponent.

[0180] By the way, since the encoding process carried out by thetransmission apparatus 10 outputs a sum of a plurality of encodedsequences, the decoder 62 ₀ described above is not capable of finding alikelihood value in a simple manner as indicated by Eq. (51) givenbefore. In order to solve this problem, the MAP decoders 84 and 86employed in the decoder 620 find a likelihood value as follows.

[0181] Let symbol L_(k) ⁽⁰⁾(+1) denotes the likelihood that thetime-axis kth constituent of a received sequence for an encoded sequencex⁽⁰⁾ is “1” and symbol L_(k) ⁽⁰⁾(−1) denotes the likelihood that thetime-axis kth constituent of a received sequence for an encoded sequencex⁽⁰⁾ is “−1”. Also assume that probabilities for other encoded sequencesx⁽¹⁾ and x⁽²⁾ have been obtained. In this case, the likelihood L_(k)⁽⁰⁾(+1) and the likelihood L_(k) ⁽⁰⁾(−1) are expressed by Eqs. (52) and(53) given below. It should be noted that the likelihood L⁽⁰⁾(+1) andthe likelihood L_(k) ⁽⁰⁾(−1) are each normalized so that, eventually,their sum becomes equal to 1. $\begin{matrix}{{L_{k}^{(0)}\left( {+ 1} \right)} = {{p\left( {\left. y_{k} \middle| x_{k}^{(0)} \right. = {+ 1}} \right)} \propto {{P\left( {x_{k}^{(1)} = {+ 1}} \right)}{P\left( {x_{k}^{(2)} = {+ 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - \left( {{a^{(0)}\left( {+ 1} \right)} + {a^{(1)}\left( {+ 1} \right)} + {a^{(2)}\left( {+ 1} \right)}} \right.^{2}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {- 1}} \right)}{P\left( {x_{k}^{(2)} = {- 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - \left( {{a^{(0)}\left( {+ 1} \right)} + {a^{(1)}\left( {- 1} \right)} + {a^{(2)}\left( {+ 1} \right)}} \right.^{2}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {+ 1}} \right)}{P\left( {x_{k}^{(2)} = {- 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - \left( {{a^{(0)}\left( {+ 1} \right)} + {a^{(1)}\left( {+ 1} \right)} + {a^{(2)}\left( {- 1} \right)}} \right.^{2}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {- 1}} \right)}{P\left( {x_{k}^{(2)} = {- 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack \quad {\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - \left( {{a^{(0)}\left( {+ 1} \right)} + {a^{(1)}\left( {- 1} \right)} + {a^{(2)}\left( {- 1} \right)}} \right.^{2}} \right\rbrack} \right.}}} \right.}}} \right.}}} \right.}}}} & (52) \\{{L_{k}^{(0)}\left( {- 1} \right)} = {{p\left( {\left. y_{k} \middle| x_{k}^{(0)} \right. = {- 1}} \right)} \propto {{P\left( {x_{k}^{(1)} = {+ 1}} \right)}{P\left( {x_{k}^{(2)} = {+ 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - \left( {{a^{(0)}\left( {- 1} \right)} + {a^{(1)}\left( {+ 1} \right)} + {a^{(2)}\left( {+ 1} \right)}} \right.^{2}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {- 1}} \right)}{P\left( {x_{k}^{(2)} = {+ 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - \left( {{a^{(0)}\left( {- 1} \right)} + {a^{(1)}\left( {- 1} \right)} + {a^{(2)}\left( {+ 1} \right)}} \right.^{2}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {+ 1}} \right)}{P\left( {x_{k}^{(2)} = {- 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - \left( {{a^{(0)}\left( {- 1} \right)} + {a^{(1)}\left( {+ 1} \right)} + {a^{(2)}\left( {- 1} \right)}} \right.^{2}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {- 1}} \right)}{P\left( {x_{k}^{(2)} = {- 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack \quad {\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - \left( {{a^{(0)}\left( {- 1} \right)} + {a^{(1)}\left( {- 1} \right)} + {a^{(2)}\left( {- 1} \right)}} \right.^{2}} \right\rbrack} \right.}}} \right.}}} \right.}}} \right.}}}} & (53)\end{matrix}$

[0182] That is to say, the likelihood L_(k) ⁽⁰⁾(+1) and the likelihoodL_(k) ⁽⁰⁾(−1) are each found by first finding a degree of likelihoodwith receive symbols compared for each of all possible candidates fortransmit symbols and then adding the degrees of likelihood, which areeach weighted by a probability of the transmit symbol's beingtransmitted. In this case, the probability of a transmit symbol's beingtransmitted can be found by multiplying probabilities, which are each aprobability that a constituent of the encoded sequence x<⁰) istransmitted. In the case of a code decoded before, its probability isused. In the case of a code not decoded before, on the other hand, avalue representing an unknown probability is reflected.

[0183] It should be noted that, in the case of a transmission through acommunication line with variations in amplitude existing, the likelihoodL_(k) ⁽⁰⁾(+1) and the likelihood L_(k) ⁽⁰⁾(−1) can be found by using byEqs. (54) and (55) given below. It is worth noting that symbol f_(k)used in Eqs. (54) and (55) denotes the amplitude of a kth constituent onthe communication line. $\begin{matrix}{{L_{k}^{(0)}\left( {+ 1} \right)} = {{p\left( {\left. y_{k} \middle| x_{k}^{(0)} \right. = {+ 1}} \right)} \propto {{P\left( {x_{k}^{(1)} = {+ 1}} \right)}{P\left( {x_{k}^{(2)} = {+ 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - {f_{k} \cdot \left( {{a^{(0)}\left( {+ 1} \right)} + {a^{(1)}\left( {+ 1} \right)} + {a^{(2)}\left( {+ 1} \right)}} \right.^{2}}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {- 1}} \right)}{P\left( {x_{k}^{(2)} = {- 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - {f_{k} \cdot \left( {{a^{(0)}\left( {+ 1} \right)} + {a^{(1)}\left( {- 1} \right)} + {a^{(2)}\left( {+ 1} \right)}} \right.^{2}}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {+ 1}} \right)}{P\left( {x_{k}^{(2)} = {- 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - {f_{k} \cdot \left( {{a^{(0)}\left( {+ 1} \right)} + {a^{(1)}\left( {+ 1} \right)} + {a^{(2)}\left( {- 1} \right)}} \right.^{2}}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {- 1}} \right)}{P\left( {x_{k}^{(2)} = {- 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack \quad {\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - {f_{k} \cdot \left( {{a^{(0)}\left( {+ 1} \right)} + {a^{(1)}\left( {- 1} \right)} + {a^{(2)}\left( {- 1} \right)}} \right.^{2}}} \right\rbrack} \right.}}} \right.}}} \right.}}} \right.}}}} & (54) \\{{L_{k}^{(0)}\left( {- 1} \right)} = {{p\left( {\left. y_{k} \middle| x_{k}^{(0)} \right. = {- 1}} \right)} \propto {{P\left( {x_{k}^{(1)} = {+ 1}} \right)}{P\left( {x_{k}^{(2)} = {+ 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - {f_{k} \cdot \left( {{a^{(0)}\left( {- 1} \right)} + {a^{(1)}\left( {+ 1} \right)} + {a^{(2)}\left( {+ 1} \right)}} \right.^{2}}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {- 1}} \right)}{P\left( {x_{k}^{(2)} = {+ 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - {f_{k} \cdot \left( {{a^{(0)}\left( {- 1} \right)} + {a^{(1)}\left( {- 1} \right)} + {a^{(2)}\left( {+ 1} \right)}} \right.^{2}}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {+ 1}} \right)}{P\left( {x_{k}^{(2)} = {- 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack {{\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - {f_{k} \cdot \left( {{a^{(0)}\left( {- 1} \right)} + {a^{(1)}\left( {+ 1} \right)} + {a^{(2)}\left( {- 1} \right)}} \right.^{2}}} \right\rbrack} + {{P\left( {x_{k}^{(1)} = {- 1}} \right)}{P\left( {x_{k}^{(2)} = {- 1}} \right)}\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp\left\lbrack \quad {\frac{- 1}{2\sigma_{n}^{2}}\left. {y_{k} - {f_{k} \cdot \left( {{a^{(0)}\left( {- 1} \right)} + {a^{(1)}\left( {- 1} \right)} + {a^{(2)}\left( {- 1} \right)}} \right.^{2}}} \right\rbrack} \right.}}} \right.}}} \right.}}} \right.}}}} & (55)\end{matrix}$

[0184] The MAP decoders 84 and 86 employed in the decoder 620 findposteriori probability information by using the likelihood L_(k) ⁽⁰⁾(+1)and the likelihood L_(k) ⁽⁰⁾(−1) computed in the way described above.

[0185] By providing the decoder 62 ₀ with the MAP decoders 84 and 86serving as counterparts of respectively the element encoders 21 ₀ and 21₁ employed in the converter 11 _(j), the decoder 62 ₀ including the MAPdecoders 84 and 86 is capable of improving characteristics from time totime due to interactions between the MAP decoders 84 and 86 bydecomposition of code with a high degree of decoding complexity intoelements each having a low degree of complexity. When the decoder 62 ₀receives the received value y, the decoder 62 ₀ carries out a repetitivedecoding process repeatedly a predetermined plurality of times and, onthe basis of external information of a soft-output obtained as a resultof this decoding process, the decoder 62 ₀ generates the posterioriprobability information P(b⁽⁰⁾|y) for the information-bit sequence b⁽⁰⁾from the MAP decoder 86 as decoded data and, if necessary, outputs theposteriori probability information P(x⁽⁰⁾|y) for the encoded sequencex⁽⁰⁾ to the other decoders 62 ₁ and 62 ₂.

[0186] In the reception apparatus 60, the decoders 62 ₁ and 62 ₂ eachhave the same configuration as the decoder 62 ₀. That is to say, byusing the likelihood L_(k) ⁽¹⁾(+1) and the likelihood L_(k) ⁽¹⁾(−1),which are found in accordance with Eqs. (52), (53), (54) and (55), thedecoder 62 ₁ generates the posteriori probability information P(b⁽¹⁾|y)for the information-bit sequence b⁽¹⁾ and the posteriori probabilityinformation P(x⁽¹)|y) for the encoded sequence x⁽¹⁾. The decoder 62 ₁then outputs the posteriori probability information P(b⁽¹⁾|y) as decodeddata and, if necessary, supplies the posteriori probability informationP(x⁽¹⁾|y) to the decoders 62 ₀ and 62 ₂. By the same token, by using thelikelihood L_(k) ⁽²⁾(+1) and the likelihood L_(k) ⁽²⁾(−1), which arefound in accordance with Eqs. (52), (53), (54) and (55), the decoder 62₂ generates the posteriori probability information P(b⁽²⁾|y) for theinformation-bit sequence b⁽²⁾ and the posteriori probability informationP(x⁽²⁾|y) for the encoded sequence x⁽²⁾. The decoder 622 then outputsthe posteriori probability information P(b⁽²⁾|y) as decoded data and, ifnecessary, supplies the posteriori probability information P(x⁽²⁾|y) tothe decoders 62 ₀ and 62 ₁.

[0187] As described above, by sequentially finding the pieces ofposteriori probability information P(b⁽²⁾|y), posteriori probabilityinformation P(b⁽¹⁾|y) and posteriori probability information P(b⁽⁰⁾|y)for the information-bit sequences b⁽²⁾, b⁽¹⁾ and b⁽⁰⁾ respectively, thereception apparatus 60 employing the decoders 62 ₀, 62 ₁ and 62 ₂ iscapable of carrying out decoding processes to generate theinformation-bit sequences b⁽²⁾, b⁽¹⁾ and b⁽⁰⁾ in an order theinformation-bit sequences b⁽²⁾, b⁽¹⁾ and b⁽⁰⁾ are enumerated here.

[0188] In addition, the reception apparatus 60 does not carry out adecoding process only once sequentially to generate information-bitsequences starting with the information-bit sequence b⁽²⁾. Instead, thereception apparatus 60 is capable of performing the zigzag decodingprocess or the repetitive decoding process as described above.

[0189] To put it concretely, as described above, the reception apparatus60 basically carries out A, B and C in an order A, B and C areenumerated, where A, B and C denote the decoding processes carried outby the decoders 62 ₀, 62 ₁ and 62 ₂ respectively. Upon completion of Aand B, A can also be carried out again by supplying the posterioriprobability information P(x⁽¹⁾|y) obtained for the encoded sequence x⁽¹⁾to the decoder 62 ₂ as priori probability information P(x⁽¹⁾) for theencoded sequence x⁽¹⁾. In this way, the reception apparatus 60 iscapable of improving the reliability of the decoding process of theencoded sequence x⁽²⁾. Thus, the reception apparatus 60 is also capableof improving the reliabilities of the decoding processes of thelower-order encoded sequences x⁽¹⁾ and x⁽⁰⁾. By the same token, uponcompletion of A, B and C, B can also be carried out again by supplyingthe posteriori probability information P(x⁽⁰⁾|y) obtained for theencoded sequence x⁽⁰⁾ to the decoder 62 ₁ as priori probabilityinformation P(x⁽⁰⁾) for the encoded sequence x⁽⁰⁾. In this way, thereception apparatus 60 is capable of improving the reliability of thedecoding process of the encoded sequence x⁽¹⁾ That is to say, thereception apparatus 60 is capable of carrying out the decoding processesin the following order: A, B, A, B, C, B and C.

[0190] As an alternative, upon completion of decoding processes A, B andC, the reception apparatus 60 may carry out these decoding processesrepeatedly a plurality of times in the following order: A, B, C, A, B, Cand so on. As another alternative, upon completion of decoding processesA, B, A, B, C, B and C, the reception apparatus 60 may carry out thesedecoding processes repeatedly a plurality of times in the followingorder: A, B, A, B, C, B, C, A, B, A, B, C, B, C and so on.

[0191] As described above, the reception apparatus 60 does not carry outa decoding process only once sequentially to generate information-bitsequences starting with the information-bit sequence b⁽²⁾. Instead, thereception apparatus 60 is capable of performing the zigzag decodingprocess or the repetitive decoding process on the basis of apredetermined rule.

[0192] By adopting methods described below in the process carried out bythe reception apparatus 60 to find a likelihood value, the process canbe made simple.

[0193] In the first place, in accordance with a first method, if anencoded sequence for which the decoding process has been completedexists, a constituent x_(k) ⁽¹⁾ maximizing the posteriori probabilityinformation P(x_(k) ⁽¹⁾) for the kth constituent is selected as the bestcandidate as shown in Eq. (56) given below. Then, the best candidate isused as priori probability information X_(k.best) ⁽¹⁾ in finding alikelihood value for another encoded sequence. That is to say, inaccordance with the first method, for an encoded sequence for which thedecoding process has been completed, a hard decision is made.$\begin{matrix}{x_{k \cdot {best}}^{(l)} = {\max\limits_{x_{k}^{(l)}}\left\lbrack {P\left( x_{k}^{(l)} \right)} \right\rbrack}} & (56)\end{matrix}$

[0194] For example, when A and C of decoding processes A, B and Ccarried out by the aforementioned decoders 62 ₀, 62 ₁ and 62 ₂respectively are completed, the decoder 62 ₁ finds the likelihood of theconstituent x_(k) ⁽¹⁾ in accordance with Eq. (57) given below. If thedecoder 62 ₁ regards the priori probability information for the bestcandidate in the encoded sequences x⁽⁰⁾ and x⁽²⁾, for which the decodingprocesses have been completed, as information having a value of 1 andthe priori probability information for other constituents as informationhaving a value of 0, Eqs. (52) and (53) given before can be simplified.$\begin{matrix}{{p\left( y_{k} \middle| x_{k}^{(l)} \right)} \propto {\frac{1}{\sqrt{2\pi}\sigma_{n}}{\exp \left\lbrack {\frac{- 1}{2\sigma_{n}^{2}}{{y_{k} - \left( {{a^{(0)}x_{k \cdot {best}}^{(0)}} + {a^{(1)}x_{k}^{(1)}} + {a^{(2)}x_{k \cdot {best}}^{(2)}}} \right)}}^{2}} \right\rbrack}}} & (57)\end{matrix}$

[0195] In the second place, in accordance with a second method, if anencoded sequence for which the decoding process has been completedexists, an expected value for a kth constituent, for which a harddecision has been made, is found as posteriori probability informationas shown in Eq. (57) given below. Then, the posteriori probabilityinformation is used as priori probability information x_(k.exp) ⁽¹⁾ infinding a likelihood value for another encoded sequence. $\begin{matrix}{x_{k \cdot \exp}^{(1)} = {\sum\limits_{x_{k}^{(l)}}{{P\left( x_{k}^{(l)} \right)}x_{k}^{(l)}}}} & (58)\end{matrix}$

[0196] For example, when A and C of decoding processes A, B and Ccarried out by the aforementioned decoders 62 ₀, 62 ₁ and 62 ₂respectively are completed, the decoder 62 ₁ finds the likelihood of theconstituent x_(k) ⁽¹⁾ in accordance with Eq. (59) given below. In thisway, Eqs. (52) and (53) given before can be simplified. $\begin{matrix}{{p\left( y_{k} \middle| x_{k}^{(1)} \right)} \propto {\frac{1}{\sqrt{2{\pi\sigma}_{n}}}{\exp \left\lbrack {\frac{- 1}{2\sigma_{n}^{2}}{{y_{k} - \left( {{a^{(0)}x_{k - \exp}^{(0)}} + {a^{(1)}x_{k}^{(1)}} + {a^{(2)}x_{k - \exp}^{(2)}}} \right)}}^{2}} \right\rbrack}}} & (59)\end{matrix}$

[0197] In the third place, in accordance with a third method, if anattempt is made to decode an encoded sequence and other encodedsequences have not been encoded, the other encoded sequences areregarded as Gaussian noises having equal electric power.

[0198] For example, if the decoder 622 computes the likelihood of theconstituent x_(k) ⁽²⁾ in accordance with Eq. (60) given below indecoding process C of the decoder 62 ₂, Eqs. (52) and (53) given earliercan be simplified. It should be noted that, in this case, if encodedsequences for which the decoding process has been completed exist, thefirst or second methods can be applied to these encoded sequences.$\begin{matrix}{{p\left( y_{k} \middle| x_{k}^{(1)} \right)} \propto {\frac{1}{\sqrt{2{\pi \left( {\sigma_{n}^{2} + a^{{(1)}^{2}} + a^{{(0)}^{2}}} \right)}}}{\exp \left\lbrack {\frac{- 1}{2\left( {\sigma_{n}^{2} + a^{{(1)}^{2}} + a^{{(0)}^{2}}} \right)}{{y_{k} - {a^{(2)}x_{k}^{(2)}}}}^{2}} \right\rbrack}}} & (60)\end{matrix}$

[0199] By the way, if a gain or a loss exists on the communication lineinvolved in a decoding process, the reception apparatus 60 needs tograsp the value of the gain or the loss. A method of estimating a gainor a loss on a communication line is explained as follows.

[0200] Normally, a gain or a loss of a communication line is estimatedby using a pilot signal provided separately from encoded sequences. Withthis method, however, the use of numerous pilot signals entailsundesirable consumption of large energy for transmitting the signals.

[0201] In order to solve this problem, a channel estimation unit 90 isprovided for at least the decoder 62 ₂ as shown in FIG. 16 for makingthe reception apparatus 60 capable of estimating a gain or a loss of thecommunication line.

[0202] The decoder 62 ² employed in the reception apparatus 60 decodesthe encoded sequence x⁽²⁾ having a largest amplitude after an estimationprocess of an amplitude f sufficiently accurate for the decoding processof the encoded sequence x⁽²⁾ The estimation process is carried out by anestimator 91 by adoption of a method such as a technique of using apilot signal or a technique of determining the magnitude of the receivedvalue y. Then, upon completion of the decoding process of the encodedsequence x⁽²⁾, the reception apparatus 60 finds a hard-decision-valuesequence x⁽²⁾, which is an estimated value of the encoded sequence x⁽²⁾,through execution of a re-encoding process g in a converter 92 by usingposteriori probability information p(b⁽²⁾|y) for an information-bitsequence b⁽²⁾ obtained as a result of the decoding process as shown byEqs. (61) and (62) as follows: $\begin{matrix}{b^{{(2)}^{\prime}} = {\max\limits_{b}\left\lbrack {p\left( {b^{(2)}\left. y \right)} \right\rbrack} \right.}} & (61)\end{matrix}$

x ^((2)′) =g(b ^((2)′))  (62)

[0203] Then, a correlation calculator 93 employed in the receptionapparatus 60 finds a correlation between the hard-decision-valuex^((2)′) and the received value y. The received value y is expressed byEq. (63) given below where symbol f denotes the amplitude of thecommunication line. If the hard-decision-value x^((2)′) does not includean error, a correlation f′ can be found in accordance with Eq. (64)given below. It is to be noted that symbol “.” used in Eq. (64) denotesan operation to produce an inner product. A denominator in Eq. (64) isused for normalizing the magnitude. In addition, since the encodedsequence x⁽²⁾ is an M-dimensional vector, |x⁽²⁾|² can be replaced by M.

y=f(a ⁽⁰⁾ x ⁽⁰⁾ +a ⁽¹⁾ x ⁽¹⁾ +a ⁽²⁾ x ⁽²⁾)+n  (63) $\begin{matrix}\begin{matrix}{f^{\prime} = {\frac{y \cdot x^{(2)}}{a^{(2)}{x^{(2)}}^{2}} = \frac{{{f \cdot a^{(0)}}{x^{(0)} \cdot x^{(2)}}} + {{f \cdot a^{(1)}}{x^{(1)} \cdot x^{(2)}}} + {{f \cdot a^{(2)}}{x^{(2)} \cdot x^{(2)}}} + {nx}^{(1)}}{a^{(2)}M}}} \\{= \frac{{{f \cdot a^{(0)}}{x^{(0)} \cdot x^{(2)}}} + {{f \cdot a^{(1)}}{x^{(1)} \cdot x^{(2)}}} + {{f \cdot a^{(2)}}M} + {nx}^{(2)}}{a^{(2)}M}} \\{= {f + \frac{{{f \cdot a^{(0)}}{x^{(0)} \cdot x^{(2)}}} + {{f \cdot a^{(1)}}{x^{(1)} \cdot x^{(2)}}} + {nx}^{(2)}}{a^{(2)}M}}} \\\left. \rightarrow {f\left( M\rightarrow\infty \right)} \right.\end{matrix} & (64)\end{matrix}$

[0204] That is to say, since the encoded sequences x⁽⁰⁾ and x⁽²⁾ areindependent of the encoded sequence x⁽²⁾, by setting M in thecorrelation value f′ found by using Eq. (64) at a large value, thereception apparatus 60 is capable of estimating the amplitude f of thecommunication line with a high degree of accuracy.

[0205] In addition, since a channel estimation unit 100 is employed inat least the decoder 62 ₂ as shown in FIG. 17, the reception apparatus60 is capable of estimating the communication line.

[0206] That is to say, the decoder 62 ₂ employed in the receptionapparatus 60 decodes the encoded sequence x⁽²⁾having a largest amplitudeafter an estimation process of an amplitude f sufficiently accurate forthe decoding process of the encoded sequence x⁽²⁾ Much like the channelestimation unit 90, the estimation process is carried out by anestimator 101 by adoption of a method such as a technique of using apilot signal or a technique of determining the magnitude of the receivedvalue y. Then, upon completion of the decoding process of the encodedsequence x⁽²⁾, an encoded-sequence estimator 102 employed in thereception apparatus 60 finds a hard-decision-value sequence x⁽²⁾, whichis an estimated value of the encoded sequence x⁽²⁾, by using posterioriprobability information p(x⁽²⁾|y) for the encoded sequence x⁽²⁾ as shownby Eq. (65) as follows:

x ^((2)′)=max [p(x ⁽²⁾ |y)]  (65)

[0207] Then, much like the channel estimation unit 90, a correlationcalculator 103 employed in the reception apparatus 60 finds acorrelation between the hard-decision-value sequence x⁽²⁾ and thereceived value y. As a result, the reception apparatus 60 is capable ofestimating the amplitude f of the communication line with a high degreeof accuracy.

[0208] By using the amplitude f estimated as described above, thedecoders 62 ₁ and 62 ₀ employed in the reception apparatus 60 decode theencoded sequences x⁽¹⁾ and x⁽⁰⁾ respectively. In addition, the decoder622 employed in the reception apparatus 60 may again decode the encodedx⁽²⁾ by using the estimated amplitude f.

[0209] The data transmission and reception system comprising thetransmission apparatus 10 for carrying out encoding processes describedearlier and the reception apparatus 60 for carrying out decodingprocesses explained above is capable of setting the constant a⁽¹⁾adaptively to changes in communication-line state as follows. In amobile communication, for example, a channel model varies in accordancewith the movement speed of the moving body. In a stationary state, thechannel model is a static channel. In the state of a high-speedmovement, on the other hand, the channel model is a Rayleigh channel. Ina such case, the transmission apparatus 10 had rather change theconstant a⁽¹⁾ in accordance with the communication line to give a goodcharacteristic. By the constant a⁽¹⁾, which is a parameter of theencoding process, the amplitude of the encoded sequence x⁽¹⁾ is meant.

[0210] When the channel model of the data transmission and receptionsystem varies, a state of the communication line is discriminated and aparameter a⁽¹⁾ optimum for the communication line is found. Then, anencoding process is carried out in accordance with the constant a⁽¹⁾.

[0211] As an adaptive encoding method, there is conceived an encodingtechnique whereby the reception apparatus identifies a state of thecommunication line, feeding the state of the communication line back tothe transmission apparatus as feedback information in the so-calledduplex communication, and the transmission apparatus adaptivelyimplements the encoding technique based on the feedback information.

[0212] To put it concretely, in the reception apparatus 60 of a typicaldata transmission and reception system, the outline of which is shown inFIG. 18, a channel estimation unit identifies a state of thecommunication line and a controller 150 ₁ determines a constant a⁽¹⁾,which is a parameter of the encoding process, on the basis of thediscriminated state. In the reception apparatus 60 of the datatransmission and reception system, the determined constant a⁽¹⁾ is usedin a decoding process carried out by a decoder as a parameter PRc of thecurrent time. The determined constant a⁽¹⁾ is also transmitted to thetransmission apparatus as a parameter PR_(N) of a next time. It is to benoted that the decoder employed in the reception apparatus 60corresponds to the decoders 62 ₀, 62 ₁ and 62 ₂ described earlier.

[0213] Then, when the transmission apparatus 10 of the data transmissionand reception system receives the parameter PR_(N) of a next time fromthe reception apparatus 60, in the transmission apparatus 10, theparameter PR_(N) of a next time is passed on to an encoder as aparameter PR_(C) of the current time by way of a controller 150 ₂. Theencoder then carries out an encoding process by using the parameterPR_(C) of the current time, and transmits a result of the encodingprocess to the reception apparatus 60 by way of the communication line.It is to be noted that the encoder employed in the transmissionapparatus 10 corresponds to the converters 11 ₀, 11 ₁ and 11 ₂, themultipliers 12 ₀, 12 ₁ and 12 ₂ as well as the adders 13 ₀ and 13 ₁,which have been described earlier.

[0214] As described above, when a duplex communication is carried out inthe data transmission and reception system, the reception apparatusidentifies a state of the communication line, feeding the state of thecommunication line back to the transmission apparatus as feedbackinformation, and the transmission apparatus carries out an encodingprocess based on the feedback information in an adaptive manner, makingit possible to improve the characteristic.

[0215] In addition, as an adaptive encoding technique, there is alsoconceived a method whereby the transmission apparatus identifies a stateof a communication line being used for reception, and assumes that thestate of a communication line for transmission is the same as the stateof the communication line being used for reception, adaptively carryingout an encoding process based on information on the state of thecommunication line being used for reception.

[0216] To put it concretely, in order to give an advance notice of aparameter change as a part of an operation to change an encodingparameter in the data transmission and reception system, thetransmission apparatus 10, which is provided with a channel estimationunit and a controller 150 ₁ as shown by an outline of a typicalconfiguration of the data transmission and reception system in FIG. 19,identifies a communication line's state to be used by the controller 150₂ as a base for determining the encoding parameter, that is, theconstant a⁽¹⁾. Then, in the data transmission and reception system, thedetermined constant a⁽¹⁾ is multiplexed by a multiplexer in aninformation-bit sequence as a parameter PR_(N) of the next time and,furthermore, the constant a⁽¹⁾ received from the controller 150 ₁ isused as a parameter PR_(C) of the current time in an encoding processcarried out by an encoder on the multiplexed data generated by themultiplexer prior to a transmission of data obtained as a result of theencoding process. It is to be noted that the encoder employed in thetransmission apparatus 10 corresponds to the converters 11 ₀, 11 ₁ and11 ₂, the multipliers 12 ₀, 12 ₁ and 12 ₂ as well as the adders 13 ₀ and13 ₁, which have been described earlier.

[0217] Then, when the reception apparatus 60 of the data transmissionand reception system receives the data transmitted by the transmissionapparatus 10 through the communication line, a decoder employed in thereception apparatus 60 decodes the data. In this case, the receptionapparatus 60 of the data transmission and reception system carries outthe encoding process by using a parameter PR_(C) output by a controller150 ₂. A demultiplexer employed in the reception apparatus 60 of thedata transmission and reception system separates the parameter PR_(N)multiplexed by the transmission apparatus 10 from data obtained as aresult of the decoding process, and supplies the separated parameterPR_(N) to the controller 150 ₂, which then makes a parameter change. Indecoding processes carried out in the data transmission and receptionsystem starting from the next time, the new parameter PR_(N i)s used asthe parameter PR_(C) of the current time. It is to be noted that thedecoder employed in the reception apparatus 60 corresponds to thedecoders 620, 62 ₁ and 62 ₂ described earlier.

[0218] As described above, the transmission apparatus in the datatransmission and reception system identifies a state of a communicationline being used for reception, and assumes that the state of acommunication line for transmission is the same as the state of thecommunication line being used for reception, adaptively carrying out anencoding process based on information on the state of the communicationline being used for reception, so that the processing load of thereception apparatus can be reduced.

[0219] It is to be noted that, as the adaptive encoding process, anadvance notice of a parameter change is given. This is because it isnecessary to inform the reception apparatus in advance of a parameter tobe used in processing to decode data at the next time in the adaptiveencoding process. In the data transmission and reception system,nevertheless, it is also possible to include a parameter of the presenttime in data of the present time as follows.

[0220] To put it concretely, a data transmission and reception systemcan be configured in the same way as the data transmission and receptionsystem shown in FIG. 19 as is shown in a typical configuration outlineof FIG. 20. In this case, the reception apparatus 60 needs to decodedata in which a parameter is multiplexed. Pay attention to the factthat, in this case, the decoding process can be carried out with thehighest-order encoded sequence relatively not affected by a power ratioof a low-order encoded sequence.

[0221] In the data transmission and reception system, the transmissionapparatus 10 provided with a channel estimation unit and a controller150 ₁ identifies a state of a communication to be used by the controller150 ₁ as a base for determining the encoding parameter, that is, theconstant a⁽¹⁾. Then, the determined constant a⁽¹⁾ is multiplexed by amultiplexer in the highest-order information-bit sequence as a parameterPR_(C) of the current time and, furthermore, the constant a⁽¹⁾ receivedfrom the controller 150 ₁ is used as a parameter PR_(C) of the currenttime in an encoding process carried out by an encoder on the multiplexeddata generated by the multiplexer prior to a transmission of dataobtained as a result of the encoding process.

[0222] Then, when the reception apparatus 60 of the data transmissionand reception system receives the data transmitted by the transmissionapparatus 10 through the communication line, a decoder employed in thereception apparatus 60 decodes the highest-order encoded sequence. Inthis case, the reception apparatus 60 of the data transmission andreception system decodes the data, starting with the highest-orderencoded sequence by using a predetermined parameter PR_(C) output by acontroller 150 ₂. A demultiplexer employed in the reception apparatus 60of the data transmission and reception system separates the parameterPR_(C) multiplexed by the transmission apparatus 10 from data obtainedas a result of the decoding process, and supplies the separatedparameter PR_(C) to the controller 150 ₂, which then makes a parameterchange Thus, it is possible to carry out a process to decode an encodedsequence of an order lower than the highest-order encoded sequence byusing the new parameter PR_(C).

[0223] As described above, the transmission apparatus in the datatransmission and reception system identifies a state of a communicationline being used for reception, and assumes that the state of acommunication line for transmission is the same as the state of thecommunication line being used for reception and, in an encoding processcarried out by the reception apparatus on the basis of information onthe state of the communication line being used for reception, theparameter of the current time can be included in the highest-order theencoded sequence of the current time so that the encoding process can becarried out without the necessity to give an advance notice to thereception apparatus.

[0224] Now, in order to evaluate the performance of such a datatransmission and reception system, a characteristic used generally forshowing the code performance is found for a Rayleigh channel and an AWGNchannel by simulation. The characteristic is represented by a relationbetween a bit error rate BER and a signal-to-noise power ratioE_(b)/N_(o) per bit.

[0225] In this simulation, turbo code represented by a generatedpolynomial equation G in Eq. (66) shown below is used as raw code, aninterleaver is used for carrying out random interleaving processes amongthe converters, a transmission rate C is set at ½, a puncture patternrepresented by Eq. (67) given below is used and a channel interleaver isused for carrying out random interleaving processes among theconverters. In addition, in this simulation, the number of informationbits (N) supplied to each of the converters is set at 20,000. That is tosay, the number of constituents (M) composing an encoded sequencegenerated by each converter is set at 40,000 and the number ofrepetitions in a turbo decoding process carried out by each decoder isset at 20. $\begin{matrix}{{G(D)} = \left( \frac{\begin{matrix}1 \\{1 + D^{4}}\end{matrix}}{1 + D + D^{2} + D^{3} + D^{4}} \right)} & (66) \\{\begin{pmatrix}{INFORMATION} \\{PARITY0} \\{PARITY1}\end{pmatrix} = \begin{pmatrix}1 & 1 \\1 & 0 \\0 & 1\end{pmatrix}} & (67)\end{matrix}$

[0226] When the characteristic for an AWGN channel is found under theconditions described above, results shown in FIG. 21 were obtained. Inaddition, characteristic curves shown in FIG. 22 were also obtained.

[0227] That is to say, when a bit error rate is found as an originalAWGN characteristic of turbo code with the probability density functionof a noise expressed by Eq. (68) given below, the leftmostcharacteristic curve shown in FIG. 22, that is, a characteristic shownby a solid line, was obtained. In this case, from this channel'scharacteristic shown in FIG. 21, the constant a⁽⁰⁾ is 0.775 for ξ⁽⁰⁾=0.8dB where ξ⁽⁰⁾ is a signal-to-noise power ratio E_(b)/n_(o) required bythe signal. $\begin{matrix}{{p(n)} = {\frac{1}{\sqrt{\pi \quad n_{0}}}{\exp \left\lbrack {{- \frac{1}{n_{0}}}n_{2}} \right\rbrack}}} & (68)\end{matrix}$

[0228] Next, as a channel model, a communication line is expressed interms of a probability density function as shown in Eq. (69) givenbelow. Along the communication line, a sum of noises and a specificsequence is added. The specific sequence has the same statisticalproperties as the constant-times encoded sequence a⁽⁰⁾x⁽⁰⁾. In addition,the leftmost characteristic curve shown in FIG. 22, that is, acharacteristic shown by a dashed line, was obtained. In this case, fromthis channel characteristic, the constant a⁽¹⁾ is 1.137 for ξ⁽¹⁾=0.7 dBwhere ξ⁽¹⁾ is a signal-to-noise power ratio E_(b)/(n₀+2ν⁽⁰⁾) required bythe signal. $\begin{matrix}\begin{matrix}{{p(n)} = {\frac{1}{\sqrt{\pi \quad n_{0}}}{{\exp \left\lbrack {{- \frac{1}{n_{0}}}n^{2}} \right\rbrack} \otimes \frac{1}{2}}\left( {{\delta \left( {n + a^{(0)}} \right)} + {\delta \left( {n - a^{(0)}} \right)}} \right)}} \\{= {{\frac{1}{2\sqrt{\pi \quad n_{0}}}{\exp \left\lbrack {{- \frac{1}{n_{0}}}\left( {n + a^{(0)}} \right)^{2}} \right\rbrack}} + {\frac{1}{2\sqrt{\pi \quad n_{0}}}{\exp \left\lbrack {{- \frac{1}{n_{0}}}\left( {n + a^{(0)}} \right)^{2}} \right\rbrack}}}}\end{matrix} & (69) \\\quad & \quad\end{matrix}$

[0229] Further, as a channel model, another communication line isassumed. Along the assumed communication line, a sum of noises and aspecific sequence is added. The specific sequence has the samestatistical properties as the constant-times encoded sequences a⁽⁰⁾x⁽⁰⁾and a⁽¹⁾x⁽¹⁾. In addition, the leftmost characteristic curve shown inFIG. 22, that is, a characteristic shown by a dotted line, was obtained.In this case, from this channel characteristic shown in FIG. 21, theconstant a⁽²⁾ is 1.658 for ξ⁽²⁾=0.6 dB where ξ⁽²⁾ is a signal-to-noisepower ratio E_(b)/(n_(o)+2ν⁽¹⁾) required by the signal.

[0230] By the same token, as a channel model, a further communicationline is assumed. Along the assumed communication line, a sum of noisesand a specific sequence is added. The specific sequence has the samestatistical properties as the constant-times encoded sequences a⁽⁰⁾x⁽⁰⁾, a⁽¹⁾ x⁽¹⁾ and a⁽²⁾x⁽²⁾. In addition, the leftmost characteristiccurve shown in FIG. 22, that is, a characteristic shown by adouble-dotted line, was obtained. In this case, from this channelcharacteristic shown in FIG. 21, the constant a⁽³⁾ is 2.430 for ξ⁽³⁾=0.6dB where ξ⁽³⁾ is a signal-to-noise power ratio E_(b)/(n_(o)+2ν⁽²⁾)required by the signal.

[0231] By using these constants a⁽¹⁾, as the code, it is possibleconstruct an additive encoded sequence with a transmission rate C of 2/2by summing up 2 sequences, namely, the constant-times encoded sequencesa⁽⁰⁾x⁽⁰⁾ and a⁽¹⁾x⁽¹⁾, an additive encoded sequence with a transmissionrate C of 3/2 by summing up 3 sequences, namely, the constant-timesencoded sequences a⁽⁰⁾x⁽ ⁾a⁽¹⁾x⁽¹⁾ and a⁽²⁾x⁽²⁾ and an additive encodedsequence with a transmission rate C of 4/2 by summing up 4 sequences,namely, the constant-times encoded sequences a⁽⁰⁾x⁽⁰⁾, a⁽¹⁾x⁽¹⁾,a⁽²⁾x⁽²⁾ and a⁽³⁾x⁽³⁾. These are summarized in FIG. 21. It is to benoted that the constant-times encoded sequences a⁽⁰⁾x⁽⁰⁾, a⁽¹⁾ x⁽¹⁾,a⁽²⁾x⁽²⁾ and a⁽³⁾x⁽³⁾ are referred to as stage 0, stage 1, stage 2 andstage 3 respectively. It is also worth noting that, in the same figure,average signal-to-noise power ratios E_(b)/n₀=ξ_(ave′) expected andrequired in transmissions of additive encoded sequences are also shown.

[0232] Characteristic curves shown in FIG. 22 were obtained as a resultof processing to find characteristics of sequences in an AWGN channel bychanging the noise power density n_(o) through the use of code designedas described above.

[0233] In addition, under the same conditions, by assuming that theestimation of a communication line is perfect, characteristics in afully-interleaved Rayleigh channel were also found. As shown in FIG. 23,the constant a⁽⁰⁾ is 0.965 for ξ⁽⁰⁾=2.7 dB where ξ⁽⁰⁾ is asignal-to-noise power ratio E_(b)/n_(o) required by the signal, theconstant a⁽¹⁾ is 1.489 for ξ⁽¹⁾=1.9 dB where ξ⁽¹⁾ is a signal-to-noisepower ratio E_(b)/(n_(o)+2ν⁽⁰⁾) required by the signal, the constanta⁽²⁾ is 2.167 for ξ⁽²⁾=1.1 dB where ξ⁽²⁾ is a signal-to-noise powerratio E_(b)/(n_(o)+2ν⁽¹⁾) required by the signal and the constant a⁽³⁾is 3.242 for ξ⁽³⁾=1.0 dB where ξ⁽³⁾ is a signal-to-noise power ratioE_(b)/(n_(o)+2ν⁽²⁾) required by the signal.

[0234] Characteristic curves shown in FIG. 24 were obtained as a resultof processing to find characteristics of sequences in a Rayleigh channelby changing the noise power density n_(o) through the use of codedesigned as described above.

[0235] As is obvious from the characteristics shown in FIGS. 22 and 24,the value of the required signal-to-noise power ratio E_(b)/(n_(o)+2ν)is known to decrease in proportion to the number of constant-timesencoded sequences to be summed up, that is, the larger the number ofstages, the smaller the value of the required signal-to-noise powerratio E_(b)/(n_(o)+2ν). This is because, as the number of constant-timesencoded sequences to be summed up increases, the state of thecommunication line is not the state of a Gaussian distribution any more.In addition, the value of the required signal-to-noise power ratioE_(b)/(n_(o)+2ν) decreases in proportion to the number of constant-timesencoded sequences to be summed up in the case of a Rayleigh channel at adecreasing rate greater than the decreasing rate at which the value ofthe required signal-to-noise power ratio E_(b)/(n_(o)+2ν) decreases inproportion to the number of constant-times encoded sequences to besummed up in the case of an AWGN channel. This is because, in additionto the fact that, as the number of constant-times encoded sequences tobe summed up increases, the state of the communication line is not thestate of a Gaussian distribution any more, the deviation of variationsof the code decreases as described above. It is to be noted that, fromresults of the simulation, the ambiguity of a decoding result ofhigh-order code is known to have an effect on a decoding process oflow-order code. For this reason, as a constant a⁽¹⁾ for high-order code,a big margin is considered to be effective.

[0236] As described above, in the data transmission and receptionsystem, it is obvious that code with a large transmission rate can beconstructed with ease by using code having a small transmission rateand, thus, a decoding process can be carried out with high performance.

[0237] It is to be noted that, in the simulation, the encodingparameters such as the constant a⁽¹⁾ have been optimized in dependenceon whether the communication line is a static or Rayleigh channel. If acharacteristic of a static channel is predicted by using an encodingparameter for a Rayleigh channel, results shown in FIG. 25 will beobtained. That is to say, in this case, for code of 1 or more stages,the value of the required signal-to-noise power ratio E_(b)/(n_(o)+2ν)of a Raleigh channel is greater than the value of the requiredsignal-to-noise power ratio E_(b)/(n_(o)+2ν) of a static channel. Inaddition, the value of the signal-to-noise power ratio E_(b)/n_(o)required of the code at stage 0 is 2.7 dB, which is greater than thevalue of 0.8 dB shown in FIG. 21 by 1.9 dB. Thus, the characteristic inthe static channel is predicted to become equal to the value of therequired signal-to-noise power ratio E_(b)/(n_(o)+2ν), which is smallerthan the characteristic in the Rayleigh channel by at least 1.9 dB.

[0238] As described above, in the data transmission and receptionsystem, a plurality of information-bit sequences {b⁽⁰⁾, b⁽¹⁾, . . . ,b^((L−1))} is subjected to a conversion process including apredetermined encoding process and/or a predetermined modulation processto produce encoded sequences {x⁽⁰⁾, x⁽¹⁾, . . . , x^((L−1))}, which arethen multiplied by constants {a⁽⁰⁾, a⁽¹⁾, . . . , a^((L−1))}respectively to generate constant-times encoded sequences {a⁽⁰⁾x⁽⁰⁾,a⁽¹⁾x⁽¹⁾, . . . , a^((L−1))x^((L−1))} respectively. The constant-timesencoded sequences {a⁽⁰⁾x⁽⁰⁾, a⁽¹⁾x⁽¹⁾, . . . , a^((L−1))x^((L−1))} arethen summed up to produce an additive encoded sequence g, which isfinally transmitted. Thus, there are only few limitations on theoriginal code, which serves as the basic, making it possible to easilyimplement a high-performance encoding process allowing the freedom ofthe code design to be enhanced considerably. As a result, theinformation-bit sequences {b⁽⁰⁾, b⁽¹⁾, . . . , b^((L−1))} can be encodedin such an optimum manner that the value of the signal-to-noise powerratio E_(b)/n_(o) required for sufficiently reducing the bit error ratecan be reduced.

[0239] In addition, in the data transmission and reception system, thereception apparatus carries out decoding processes sequentially,starting with the highest-order information-bit sequence b^((L−1)).Thus, a decoding process to generate at least one information-bitsequence b⁽¹⁾ can be carried out with a high degree of precision andwith ease. In particular, in the data transmission and reception system,the reception apparatus carries out a MAP decoding process or a decodingprocess conforming to the MAP decoding process so that a decodingprocess of actual code can be performed. In addition, in the datatransmission and reception system, in a process carried out by thereception apparatus to decode any encoded sequence, information on anyother encoded sequences is used to reduce the value of thesignal-to-noise power ratio E_(b)/n_(o) required for sufficientlyreducing the bit error rate.

[0240] Thus, if it is necessary to transmit data by using a limitednumber of real numbers caused by typically the fact that the band islimited in the data transmission and reception system, it is possible tosufficiently meet a demand for an encoding process at a hightransmission rate. It is thus possible to provide much convenience tothe user.

[0241] In the embodiment described above, the amplitude of the originalsignal basically exhibits a Gaussian distribution. It is to be noted,however, that the amplitude of ordinary code does not exhibit a Gaussiandistribution. In the case of code with a low transmission rate inparticular, the BPSK modulation technique is adopted. In such a case, inthe encoding process, it is undesirable to find energy of the code onthe basis of energy of code subjected to an addition process previously.

[0242] In this case, the binary distribution entropy of signal pointsaccording to the BPSK modulation technique is 1, which lower than aGaussian distribution entropy of (½) log₂ (πe)=1.65. Thus, even if theamplitude of an encoded sequence for each information-bit sequence doesnot exhibit a Gaussian distribution, the amplitude can be made appear toexhibit a Gaussian distribution by carrying out a random normalizedconversion process on it except a fading channel. Accordingly, it isobvious that a result, which is worse than a result obtained by assumingthat each code exhibits a Gaussian distribution, is never obtained.

[0243] Therefore, it is possible to measure a value of thesignal-to-noise power ratio E_(b)/(n_(o)+2ν) required for a case, inwhich the amplitude of the original signal exhibits a non-Gaussiandistribution, by carrying out a measurement for a Gaussian channelreflecting a model of an encoder. In addition, in a decoding process, anoperation to compute a likelihood value with a high degree of accuracyin conformity with the model of the encoder is optimum.

[0244] It is to be noted that the scope of the present invention is notlimited to the embodiment described above. For example, in theembodiment described above, the turbo encoding process is adopted as theencoding process to be carried out by the converter employed in thetransmission apparatus. However, the present invention can also beapplied to any code including the Reed-Solomon code and the BCH(Bose-Chaudhuri-Hocquenghem) code.

[0245] In addition, in the embodiment described above, the BPSKmodulation technique is adopted in the encoding process to be carriedout by the converter employed in the transmission apparatus. However,the present invention can also be applied to a case in which anothermodulation technique is adopted. An example of the other modulationtechnique is the QPSK (Quadrature Phase Shift Keying) modulationtechnique. It is to be noted that, even if the QPSK modulation techniqueis adopted, signal points in the additive encoded sequence g are placeddependently on the signal-to-noise ratio S/N as described above. Forexample, the signal points are located at unequal intervals as shown inFIG. 26.

[0246] Furthermore, in the embodiment described above, only a singleinformation-bit sequence b⁽¹⁾ is supplied to a converter employed in thetransmission apparatus. In place of a single information-bit sequenceb⁽¹⁾ consisting of say 2,000 information bits, however, 2 sequences eachcomposed of 1,000 bits can be supplied to the converter. That is to say,in accordance with the present invention, an information-bit sequenceb⁽¹⁾ with any structure can be supplied to any converter as long as theencoded sequence x⁽¹⁾ output by the converter comprises M numbers.

[0247] Moreover, in the embodiment described above, a MAP decodingprocess is adopted as a typical decoding process to be carried out by adecoder employed in the reception apparatus. However, the presentinvention can also be applied for example to a case in which the Viterbidecoding process is adopted. It is to be noted that, if the Viterbidecoding process is adopted, the decoder inputs a likelihood value, butnever outputs posteriori probability information as a result of thedecoding process. For that reason, in this case, the decoder carries outa decoding process with a correct decoding result at a probability of 1.

[0248] As described above, it is needless to say that a variety ofchanges can be made appropriately within a range not departing fromessentials of the present invention.

[0249] As described above in detail, the information transmissionapparatus provided by the present invention is an informationtransmission apparatus for converting the format of input informationinto a predetermined format prior to transmission of the information.The information transmission apparatus includes: a first conversionmeans for converting a first information-bit sequence comprising apredetermined number of bits into a first encoded sequence comprising Mnumbers; a first multiplication means for multiplying the first encodedsequence produced by the first conversion means as a result of aconversion process by a first constant; at least a second conversionmeans for converting a second information-bit sequence comprising apredetermined number of bits into a second encoded sequence comprising Mnumbers; at least a second multiplication means for multiplying thesecond encoded sequence produced by the second conversion means as aresult of a conversion process by a second constant; an addition meansfor adding the constituent of a first constant-times encoded sequenceproduced by the first multiplication means as a result of amultiplication process to the constituent of a second constant-timesencoded sequence produced by the second multiplication means as a resultof a multiplication process to produce an additive encoded sequence; anda transmission means for transmitting the additive encoded sequence as atransmitted signal.

[0250] As described above, in the information transmission apparatusprovided by the present invention, the addition means adds a firstconstant-times encoded sequence produced by the first multiplicationmeans as a product of a first encoded sequence and a first constant to asecond constant-times encoded sequence produced by the secondmultiplication means as a product of a second encoded sequence and asecond constant to produce an additive encoded sequence, and thetransmission means transmits the additive encoded sequence. As a result,it is possible to easily carry out a high-performance encoding processthat allows the degree of freedom of the code design to be increasedsubstantially.

[0251] In addition, the information transmission method provided by thepresent invention is an information transmission method for convertingthe format of input information into a predetermined format prior totransmission of the information. The information transmission methodincludes: a first conversion process of converting a firstinformation-bit sequence comprising a predetermined number of bits intoa first encoded sequence comprising M numbers; a first multiplicationprocess of multiplying the first encoded sequence produced by the firstconversion process as a result of conversion by a first constant; atleast a second conversion process of converting a second information-bitsequence comprising a predetermined number of bits into a second encodedsequence comprising M numbers; at least a second multiplication processof multiplying the second encoded sequence produced by the secondconversion process as a result of conversion by a second constant; anaddition process of adding the constituent of a first constant-timesencoded sequence produced by the first multiplication process as aresult of multiplication to the constituent of a second constant-timesencoded sequence produced by the second multiplication process as aresult of multiplication to produce an additive encoded sequence; and atransmission process of transmitting the additive encoded sequence as atransmitted signal.

[0252] As described above, in the information transmission methodprovided by the present invention, a first constant-times encodedsequence produced by the first multiplication process as a product of afirst encoded sequence and a first constant is added to a secondconstant-times encoded sequence produced by the second multiplicationprocess as a product of a second encoded sequence and a second constantto produce an additive encoded sequence, and in the transmission processof the information transmission method, the additive encoded sequence istransmitted. As a result, it is possible to easily carry out ahigh-performance encoding process that allows the degree of freedom ofthe code design to be increased substantially.

[0253] In addition, the information reception apparatus provided by thepresent invention is an information reception apparatus for receiving areception signal comprising an additive encoded sequence transmitted byan information transmission apparatus and a predetermined noise added tothe additive encoded sequence includes: a first conversion means forconverting a first information-bit sequence comprising a predeterminednumber of bits into a first encoded sequence comprising M numbers; afirst multiplication means for multiplying the first encoded sequenceproduced by the first conversion means as a result of a conversionprocess by a first constant; at least a second conversion means forconverting a second information-bit sequence comprising a predeterminednumber of bits into a second encoded sequence comprising M numbers; atleast a second multiplication means for multiplying the second encodedsequence produced by the second conversion means as a result of aconversion process by a second constant; an addition means for addingthe constituent of a first constant-times encoded sequence produced bythe first multiplication means as a result of a multiplication processto the constituent of a second constant-times encoded sequence producedby the second multiplication means as a result of a multiplicationprocess to produce the additive encoded sequence; and a transmissionmeans for transmitting the additive encoded sequence as the transmittedsignal.

[0254] The information reception apparatus includes: a reception meansfor receiving the reception signal; and a decoding means for carryingout a decoding process to produce at least one of the firstinformation-bit sequence and the second information-bit sequence on thebasis of a received value received from the reception means.

[0255] As described above, the decoding means employed in theinformation reception apparatus provided by the present inventioncarries out a decoding process to produce at least one of the firstinformation-bit sequence and the second information-bit sequence on thebasis of a received value comprising an additive encoded sequence and apredetermined noise added to the additive encoded sequence produced inthe information transmission apparatus by the addition means, which addsa first constant-times encoded sequence produced by the firstmultiplication means as a result of a multiplication process to a secondconstant-times encoded sequence produced by the second multiplicationmeans as a result of a multiplication process.

[0256] In addition, the information reception method provided by thepresent invention is an information reception method for receiving areception signal comprising an additive encoded sequence and apredetermined noise added to the additive encoded sequence transmittedin accordance with an information transmission method including: a firstconversion process of converting a first information-bit sequencecomprising a predetermined number of bits into a first encoded sequencecomprising M numbers; a first multiplication process of multiplying thefirst encoded sequence produced by the first conversion process as aresult of conversion by a first constant; at least a second conversionprocess of converting a second information-bit sequence comprising apredetermined number of bits into a second encoded sequence comprising Mnumbers; at least a second multiplication process of multiplying thesecond encoded sequence produced by the second conversion process as aresult of conversion by a second constant; an addition process of addingthe constituent of a first constant-times encoded sequence produced bythe first multiplication process as a result of multiplication to theconstituent of a second constant-times encoded sequence produced by thesecond multiplication process as a result of multiplication to producean additive encoded sequence; and a transmission process of transmittingthe additive encoded sequence as the transmitted signal, wherein theinformation reception method includes: a reception process of receivingthe reception signal; and a decoding process of carrying out a decodingprocess to produce at least one of the first information-bit sequenceand the second information-bit sequence on the basis of a received valuereceived from the reception process.

[0257] As described above, the information reception method provided bythe present invention includes the decoding process carried out toproduce at least one of the first information-bit sequence and thesecond information-bit sequence on the basis of a received valuecomprising an additive encoded sequence and a predetermined noise addedto the additive encoded sequence, which is produced in accordance withthe information transmission method in the addition process carried outto add a first constant-times encoded sequence produced in the firstmultiplication process to a second constant-times encoded sequenceproduced in the second multiplication process. Accordingly, it becomespossible to carry out the decoding process to produce at least one ofthe information-bit sequence easily with a high degree of precision.

1. An information transmission apparatus for converting the format ofinput information into a predetermined format prior to transmission ofsaid information, said information transmission apparatus, comprising: afirst conversion means for converting a first information-bit sequencecomprising a predetermined number of bits into a first encoded sequencecomprising M numbers; a first multiplication means for multiplying saidfirst encoded sequence produced by said first conversion means as aresult of conversion by a first constant; at least a second conversionmeans for converting a second information-bit sequence comprising apredetermined number of bits into a second encoded sequence comprising Mnumbers; at least a second multiplication means for multiplying saidsecond encoded sequence produced by said second conversion means as aresult of conversion by a second constant; an addition means for addingthe constituent of a first constant-times encoded sequence produced bysaid first multiplication means as a result of multiplication to theconstituent of a second constant-times encoded sequence produced by saidsecond multiplication means as a result of multiplication to produce anadditive encoded sequence; and a transmission means for transmittingsaid additive encoded sequence as a transmitted signal.
 2. Aninformation transmission apparatus according to claim 1, wherein: whensaid first encoded sequence is regarded as a sequence to be transmittedthrough a communication line along which a noise is added, said firstmultiplication means multiplies said first encoded sequence by saidfirst constant set so as to sufficiently reduce a bit error rate forsaid first information-bit sequence; and when said second encodedsequence is regarded as a sequence to be transmitted through acommunication line along which a sum of said noise and a sequence havingthe same statistical characteristic as said first constant-times encodedsequence is added, said second multiplication means multiplies saidsecond encoded sequence by said second constant set so as tosufficiently reduce a bit error rate for said second information-bitsequence.
 3. An information transmission apparatus according to claim 1,wherein: when said first encoded sequence is regarded as a sequence tobe transmitted through a communication line along which a noise isadded, said first multiplication means multiplies said first encodedsequence by said first constant set so as to sufficiently reduce a biterror rate for said first information-bit sequence; and when said secondencoded sequence is regarded as a sequence to be transmitted through acommunication line along which a sum of a noise greater than said noiseby a predetermined amount and a sequence having the same statisticalcharacteristic as said first constant-times encoded sequence is added,said second multiplication means multiplies said second encoded sequenceby said second constant set so as to sufficiently reduce a bit errorrate for said second information-bit sequence.
 4. An informationtransmission apparatus according to claim 1, wherein: said firstconversion means has: a first encoding means for carrying out anencoding operation on said first information-bit sequence; and a firstmodulation means for carrying out a mapping operation of signal pointsby adoption of a predetermined modulation technique on a sequencegenerated by said first encoding means to produce said first encodedsequence comprising M numbers, whereas said second conversion means has:a second encoding means for carrying out an encoding operation on saidsecond information-bit sequence; and a second modulation means forcarrying out a mapping operation of signal points by adoption of apredetermined modulation technique on a sequence generated by saidsecond encoding means to produce said second encoded sequence comprisingM numbers.
 5. An information transmission apparatus according to claim4, wherein said first encoding means and/or said second encoding meanscarry out a parallel concatenated convolutional coding operation.
 6. Aninformation transmission apparatus according to claim 4, wherein: saidfirst encoding means and/or said second encoding means have a channelinterleave means for rearranging an order of pieces of input data on thebasis of predetermined information on permutation locations; and saidfirst modulation means and/or said second modulation means carry out amapping operation of signal points by adoption of a predeterminedmodulation technique on interleaved data generated by said channelinterleave means.
 7. An information transmission apparatus according toclaim 4, wherein said first modulation means and/or said secondmodulation means carry out a mapping operation of signal points byadoption of a 2-phase modulation technique.
 8. An informationtransmission apparatus according to claim 1, wherein: said firstmultiplication means multiplies said first encoded sequence by saidfirst constant; said second multiplication means multiplies said secondencoded sequence by said second constant; said first constant and saidsecond constant are determined on the basis of a state of acommunication line; and said state of a communication line isdiscriminated by an information reception apparatus receiving saidadditive encoded sequence.
 9. An information transmission apparatusaccording to claim 1, wherein: there is further included adiscrimination means for discriminating a state of a communication linebeing used for reception; said first multiplication means multipliessaid first encoded sequence by said first constant; said secondmultiplication means multiplies said second encoded sequence by saidsecond constant; said first constant and said second constant aredetermined on the basis of a state of said communication line being usedfor reception; and said state of a communication line being used forreception is discriminated by said discrimination means.
 10. Aninformation transmission apparatus according to claim 9, wherein: thereis provided a multiplexing means for multiplexing said determined firstconstant and said determined second constant in said highest-ordersecond information-bit sequence subjected to an addition operation lastin said addition means; and said second conversion means converts dataproduced by said multiplexing means as a result of multiplexing intosaid second encoded sequence comprising M numbers.
 11. An informationtransmission apparatus according to claim 1, wherein said firstinformation-bit sequence and said second information-bit sequence arepieces of information, which are independent of each other, or areresults of an operation to split an information-bit sequence.
 12. Aninformation transmission apparatus according to claim 1, wherein saidfirst information-bit sequence has a bit count equal to a bit count ofsaid second information-bit sequence, or said first information-bitsequence has a bit count different from a bit count of said secondinformation-bit sequence.
 13. An information transmission method forconverting the format of input information into a predetermined formatprior to transmission of said information, comprising: a firstconversion process of converting a first information-bit sequencecomprising a predetermined number of bits into a first encoded sequencecomprising M numbers; a first multiplication process of multiplying saidfirst encoded sequence produced by said first information-bit sequenceas a result of conversion by a first constant; at least a secondconversion process of converting a second information-bit sequencecomprising a predetermined number of bits into a second encoded sequencecomprising M numbers; at least a second multiplication process ofmultiplying said second encoded sequence produced by said secondinformation-bit sequence as a result of conversion by a second constant;an addition process of adding the constituent of a first constant-timesencoded sequence produced by said first multiplication process as aresult of multiplication to the constituent of a second constant-timesencoded sequence produced by said second multiplication process as aresult of multiplication to produce an additive encoded sequence; and atransmission process of transmitting said additive encoded sequence as atransmitted signal.
 14. An information transmission method according toclaim 13, wherein: when said first encoded sequence is regarded as asequence to be transmitted through a communication line along which anoise is added, in said first multiplication process of multiplying saidfirst encoded sequence by said first constant, said first encodedsequence is multiplied by said first constant set so as to sufficientlyreduce a bit error rate for said first information-bit sequence; andwhen said second encoded sequence is regarded as a sequence to betransmitted through a communication line along which a sum of said noiseand a sequence having the same statistical characteristic as said firstconstant-times encoded sequence is added, in said second multiplicationprocess of multiplying said second encoded sequence by said secondconstant, said second encoded sequence is multiplied by said secondconstant set so as to sufficiently reduce a bit error rate for saidsecond information-bit sequence.
 15. An information transmission methodaccording to claim 13, wherein: when said first encoded sequence isregarded as a sequence to be transmitted through a communication linealong which a noise is added, in said first multiplication process ofmultiplying said first encoded sequence by said first constant, saidfirst encoded sequence is multiplied by said first constant set so as tosufficiently reduce a bit error rate for said first information-bitsequence; and when said second encoded sequence is regarded as asequence to be transmitted through a communication line along which asum of a noise greater in magnitude than said noise by a predeterminedamount and a sequence having the same statistical characteristic as saidfirst constant-times encoded sequence is added in said secondmultiplication process of multiplying said second encoded sequence bysaid second constant, said second encoded sequence is multiplied by saidsecond constant set so as to sufficiently reduce a bit error rate forsaid second information-bit sequence.
 16. An information transmissionmethod according to claim 13, wherein: said first conversion process ofconverting said first information-bit sequence has: a first encodingprocess of carrying out a predetermined encoding operation on said firstinformation-bit sequence; and a first mapping process of carrying out amapping operation of signal points by adoption of a predeterminedmodulation technique on a sequence generated by said first encodingprocess to produce said first encoded sequence comprising M numbers,whereas said second conversion process of converting said secondinformation-bit sequence has: a second encoding process of carrying outa predetermined encoding operation on said second information-bitsequence; and a second mapping process of carrying out a mappingoperation of signal points by adoption of a predetermined modulationtechnique on a sequence generated by said second encoding process toproduce said second encoded sequence comprising M numbers.
 17. Aninformation transmission method according to claim 16, wherein saidfirst encoding process of carrying out a predetermined encodingoperation on said first information-bit sequence and/or said secondencoding process of carrying out a predetermined encoding operation onsaid second information-bit sequence, a parallel concatenatedconvolutional coding process is performed.
 18. An informationtransmission method according to claim 16, wherein: said first encodingprocess of carrying out a predetermined encoding operation on said firstinformation-bit sequence and/or said second encoding process of carryingout a predetermined encoding operation on said second information-bitsequence include a channel interleave process of rearranging an order ofpieces of input data on the basis of predetermined information onpermutation locations to produce interleaved data; and said firstmapping process of carrying out a mapping operation of signal points byadoption of a predetermined modulation technique on a sequence generatedby said first encoding process of carrying out a predetermined encodingoperation on said first information-bit sequence and/or said secondmapping process of carrying out a mapping operation of signal points byadoption of a predetermined modulation technique on a sequence generatedby said second encoding process of carrying out a predetermined encodingoperation on said second information-bit sequence include a mappingprocess of signal points, which is performed on said interleaved datagenerated by said channel interleave process on the basis of apredetermined modulation technique.
 19. An information transmissionmethod according to claim 16, wherein said first mapping process ofcarrying out a mapping operation of signal points by adoption of apredetermined modulation technique on a sequence generated by said firstencoding process of carrying out a predetermined encoding operation onsaid first information-bit sequence and/or said second mapping processof carrying out a mapping operation of signal points by adoption of apredetermined modulation technique on a sequence generated by saidsecond encoding process of carrying out a predetermined encodingoperation on said second information-bit sequence include a mappingprocess of signal points, which is based on a 2-phase modulationtechnique.
 20. An information transmission method according to claim 13,wherein: said first multiplication process of multiplying said firstencoded sequence by said first constant, said first encoded sequence ismultiplied by said first constant; said second multiplication process ofmultiplying said second encoded sequence by said second constant, saidsecond encoded sequence is multiplied by said second constant; saidfirst constant and said second constant are determined on the basis of astate of a communication line; and said state of a communication line isdiscriminated by an information reception apparatus receiving saidadditive encoded sequence.
 21. An information transmission methodaccording to claim 13, wherein: there is further included adiscrimination process of discriminating a state of a communication linebeing used for reception; said first multiplication process ofmultiplying said first encoded sequence by said first constant, saidfirst encoded sequence is multiplied by said first constant; said secondmultiplication process of multiplying said second encoded sequence bysaid second constant, said second encoded sequence is multiplied by saidsecond constant; said first constant and said second constant aredetermined on the basis of a state of said communication line being usedfor reception; and said state of said communication line being used forreception is discriminated in said discrimination process.
 22. Aninformation transmission method according to claim 21, wherein: there isprovided a multiplexing process of multiplexing said determined firstconstant and said determined second constant in said highest-ordersecond information-bit sequence subjected to an addition operation lastin said addition process; and in said second conversion process ofconverting said second information-bit sequence, data produced as aresult of multiplexing in said multiplexing process of multiplexing datainto said highest degree second information-bit sequence is convertedinto said second encoded sequence comprising M numbers.
 23. Aninformation transmission method according to claim 13, wherein saidfirst information-bit sequence and said second information-bit sequenceare pieces of information, which are independent of each other, or areresults of an operation to split an information-bit sequence.
 24. Aninformation transmission method according to claim 13, wherein saidfirst information-bit sequence has a bit count equal to a bit count ofsaid second information-bit sequence, or said first information-bitsequence has a bit count different from a bit count of said secondinformation-bit sequence.
 25. An information reception apparatus forreceiving a reception signal comprising an additive encoded sequence anda predetermined noise added to said additive encoded sequencetransmitted by an information transmission apparatus, comprising: afirst conversion means for converting a first information-bit sequencecomprising a predetermined number of bits into a first encoded sequencecomprising M numbers; a first multiplication means for multiplying saidfirst encoded sequence produced by said first conversion means as aresult of conversion by a first constant; at least a second conversionmeans for converting a second information-bit sequence comprising apredetermined number of bits into a second encoded sequence comprising Mnumbers; at least a second multiplication means for multiplying saidsecond encoded sequence produced by said second conversion means as aresult of conversion by a second constant; an addition means for addingthe constituent of a first constant-times encoded sequence produced bysaid first multiplication means as a result of multiplication to theconstituent of a second constant-times encoded sequence produced by saidsecond multiplication means as a result of multiplication to producesaid additive encoded sequence; and a transmission means fortransmitting said additive encoded sequence as said transmitted signal,said information reception apparatus includes: a reception means forreceiving said reception signal; and a decoding means for carrying out adecoding operation to produce at least one of said first information-bitsequence and said second information-bit sequence on the basis of areceived value received from said reception means.
 26. An informationreception apparatus according to claim 25, wherein, on the basis of saidreceived value supplied by said reception means, at least, said decodingmeans carries out a decoding operation to produce a highest-order secondinformation-bit sequence subjected to an addition operation last in saidaddition means.
 27. An information reception apparatus according toclaim 25, wherein said decoding means has a first decoding means forcarrying out a decoding operation as a counterpart operation of saidfirst conversion means and second decoding means for carrying out adecoding operation as a counterpart operation of said second conversionmeans.
 28. An information reception apparatus according to claim 27,wherein: said first decoding means carries out a decoding operation toproduce said first information-bit sequence on the basis of informationon encoded sequences other than said first encoded sequence and on thebasis of said received value; and said second decoding means carries outa decoding operation to produce said second information-bit sequence onthe basis of information on encoded sequences other than said secondencoded sequence and on the basis of said received value.
 29. Aninformation reception apparatus according to claim 28, wherein: saidsecond decoding means carries out a decoding operation to produce saidsecond information-bit sequence on the basis of information on saidfirst encoded sequence and on the basis of said received value; and saidfirst decoding means carries out a decoding operation to produce saidfirst information-bit sequence on the basis of information on saidsecond encoded sequence obtained as a result of said decoding operationcarried out by said second decoding means and on the basis of saidreceived value.
 30. An information reception apparatus according toclaim 27, wherein said first and second decoding means each have alikelihood computation means for computing a likelihood regarding areception symbol from said received value.
 31. An information receptionapparatus according to claim 30, wherein: on the basis of prioriprobability information for an encoded sequence other than said firstencoded sequence and on the basis of said received value, said firstdecoding means finds posteriori probability information for said firstinformation-bit sequence and outputs said posteriori probabilityinformation for said first information-bit sequence as a result of saiddecoding operation and finds posteriori probability information for saidfirst encoded sequence and outputs said posteriori probabilityinformation for said first encoded sequence; and on the basis of prioriprobability information for an encoded sequence other than said secondencoded sequence and on the basis of said received value, said seconddecoding means finds posteriori probability information for said secondinformation-bit sequence and outputs said posteriori probabilityinformation for said second information-bit sequence as a result of saiddecoding operation and finds posteriori probability information for saidsecond encoded sequence and outputs said posteriori probabilityinformation for said second encoded sequence.
 32. An informationreception apparatus according to claim 31, wherein: on the basis ofpriori probability information for said first encoded sequence and onthe basis of said received value, said second decoding means findsposteriori probability information for said second information-bitsequence and outputs said posteriori probability information for saidsecond information-bit sequence as a result of said decoding operationand finds posteriori probability information for said second encodedsequence and outputs said posteriori probability information for saidsecond encoded sequence to said first decoding means as prioriprobability information for said second encoded sequence; and on thebasis of the priori probability information received from said seconddecoding means for said second encoded sequence and on the basis of saidreceived value, said first decoding means finds posteriori probabilityinformation for said first information-bit sequence and outputs saidposteriori probability information for said first information-bitsequence as a result of said decoding operation and finds posterioriprobability information for said first encoded sequence and outputs saidposteriori probability information for said first encoded sequence tosaid second decoding means as priori probability information for saidfirst encoded sequence.
 33. An information reception apparatus accordingto claim 25, wherein said decoding means carries out a MAP decodingoperation or a decoding operation conforming to said MAP decodingoperation.
 34. An information reception apparatus according to claim 25,wherein said decoding means carries out decoding operations to generateinformation-bit sequences sequentially starting with a highest-ordersecond information-bit sequence subjected to an addition operation lastin said addition means.
 35. An information reception apparatus accordingto claim 25, said information reception apparatus characterized in thatsaid decoding means carries out a zigzag or repetitive decodingoperation.
 36. An information reception apparatus according to claim 25,wherein: said decoding means has a likelihood computation means forcomputing a likelihood regarding a reception symbol from said receivedvalue; and if at least one of said first encoded sequence and saidsecond encoded sequence has been encoded, said likelihood computationmeans selects a constituent that maximizes posteriori probabilityinformation for any constituent as a best candidate, and uses said bestcandidate as priori probability information for an encoded sequence tofind a likelihood for another encoded sequence.
 37. An informationreception apparatus according to claim 25, wherein: said decoding meanshas a likelihood computation means for computing a likelihood regardinga reception symbol from said received value; and if at least one of saidfirst encoded sequence and said second encoded sequence has beenencoded, said likelihood computation means finds an expected value forany arbitrary constituent already subjected to a soft decision asposteriori probability information, and uses said posteriori probabilityinformation as priori probability information for an encoded sequence tofind a likelihood for another encoded sequence.
 38. An informationreception apparatus according to claim 25, wherein: said decoding meanshas a likelihood computation means for computing a likelihood regardinga reception symbol from said received value; and if an encoded sequencenot decoded yet is found to exist in an attempt to decode one of saidfirst encoded sequence and said second encoded sequence, said likelihoodcomputation means finds a likelihood for an encoded sequence byregarding said encoded sequence not decoded yet as a Gaussian noisehaving an equal electric power.
 39. An information reception apparatusaccording to claim 25, further comprising: a re-encoding means, which isused for re-encoding a highest-order second information-bit sequence byusing posteriori probability information for said second information-bitsequence upon completion of a decoding operation carried out by saiddecoding means to produce said highest-order second information-bitsequence subjected last to an addition operation carried out by saidaddition means; a correlation computation means for finding acorrelation between a hard-decision value sequence and said receivedvalue where said a hard-decision value sequence is an estimated value ofsaid second encoded sequence obtained as a result of a re-encodingoperation carried out by said re-encoding means; and a channelestimation means for estimating an amplitude of a communication line byusing a correlation value found by said correlation computation means.40. An information reception apparatus according to claim 25, furthercomprising: a re-encoding means, which is used for re-encoding ahighest-order second information-bit sequence by using a posterioriprobability information for said second encoded sequence upon completionof a decoding operation carried out by said decoding means to producesaid highest-order second information-bit sequence subjected last to anaddition operation carried out by said addition means; a correlationcomputation means for finding a correlation between a hard-decisionvalue sequence and said received value where said a hard-decision valuesequence is an estimated value of said second encoded sequence obtainedas a result of a re-encoding operation carried out by said re-encodingmeans; and a channel estimation means for estimating an amplitude of acommunication line by using a correlation value found by saidcorrelation computation means.
 41. An information reception apparatusaccording to claim 25, wherein: there is further provided adiscrimination means for discriminating a state of a communication line;and said first and second constants are determined on the basis of astate of said communication line discriminated by said discriminationmeans.
 42. An information reception apparatus according to claim 25,wherein said reception means receives said first and second constantsdetermined on the basis of a state of a communication line discriminatedby said transmission apparatus.
 43. An information transmissionapparatus according to claim 42, wherein: said first and secondconstants determined by said information transmission apparatus aremultiplexed in a highest-order second information-bit sequence subjectedlast to an addition operation carried out by said addition means; andthere is further provided a separation means for separating said firstand second constants from said second information-bit sequence.
 44. Aninformation reception apparatus according to claim 25, wherein: whensaid first encoded sequence is regarded as a sequence to be transmittedthrough a communication line along which a noise is added, said firstmultiplication means multiplies said first encoded sequence by saidfirst constant set so as to sufficiently reduce a bit error rate forsaid first information-bit sequence; and when said second encodedsequence is regarded as a sequence to be transmitted through acommunication line along which a sum of said noise and a sequence havingthe same statistical characteristic as said first constant-times encodedsequence is added, said second multiplication means multiplies saidsecond encoded sequence by said second constant set so as tosufficiently reduce a bit error rate for said second information-bitsequence.
 45. An information reception apparatus according to claim 25,wherein: when said first encoded sequence is regarded as a sequence tobe transmitted through a communication line along which a noise isadded, said first multiplication means multiplies said first encodedsequence by said first constant set so as to sufficiently reduce a biterror rate for said first information-bit sequence; and when said secondencoded sequence is regarded as a sequence to be transmitted through acommunication line along which a sum of a noise greater than said noiseby a predetermined amount and a sequence having the same statisticalcharacteristic as said first constant-times encoded sequence is added,said second multiplication means multiplies said second encoded sequenceby said second constant set so as to sufficiently reduce a bit errorrate for said second information-bit sequence.
 46. An informationreception method for receiving a reception signal comprising an additiveencoded sequence and a predetermined noise added to said additiveencoded sequence transmitted in accordance with an transmission method,comprising: a first conversion process of converting a firstinformation-bit sequence comprising a predetermined number of bits intoa first encoded sequence comprising M-dimensional real number vector; afirst multiplication process of multiplying said first encoded sequenceproduced by said first conversion process as a result of conversion by afirst constant; at least a second conversion process of converting asecond information-bit sequence comprising a predetermined number ofbits into a second encoded sequence comprising M-dimensional real numbervector; at least a second multiplication process of multiplying saidsecond encoded sequence produced by said second conversion process as aresult of conversion by a second constant; an addition process of addingthe constituent of a first constant-times encoded sequence produced bysaid first multiplication process as a result of multiplication to theconstituent of a second constant-times encoded sequence produced by saidsecond multiplication process as a result of multiplication to producean additive encoded sequence; and a transmission process of transmittingsaid additive encoded sequence as said transmitted signal, saidinformation reception method, comprising: a reception process ofreceiving said reception signal; and a decoding process of carrying outa decoding operation to produce at least one of said firstinformation-bit sequence and said second information-bit sequence on thebasis of the received value received from said reception process.
 47. Aninformation reception method according to claim 46, wherein, on thebasis of said received value supplied by said reception process, in saiddecoding process of carrying out a decoding operation to produce atleast a information-bit sequence, at least, a decoding operation iscarried out to produce said highest-order second information-bitsequence subjected to an addition operation last in said additionprocess of producing said additive encoded sequence.
 48. An informationreception method according to claim 46, wherein said decoding process ofcarrying out a decoding operation to produce at least a information-bitsequence includes a first decoding process of carrying out a decodingoperation as a counterpart operation of said first conversion process ofconverting said first information-bit sequence and a second decodingprocess of carrying out a decoding operation as a counterpart operationof said second conversion process of converting said secondinformation-bit sequence.
 49. An information reception method accordingto claim 48, wherein: said first decoding process of carrying out adecoding operation as a counterpart operation of said first conversionprocess of converting said first information-bit sequence, a decodingoperation is performed to produce said first information-bit sequence onthe basis of encoded sequences other than said first encoded sequenceand on the basis of said received value; and said second decodingprocess of carrying out a decoding operation as a counterpart operationof said second conversion process of converting said secondinformation-bit sequence, a decoding operation is performed to producesaid second information-bit sequence on the basis of encoded sequencesother than said second encoded sequence and on the basis of saidreceived value.
 50. An information reception method according to claim49, wherein: said second decoding process of carrying out a decodingoperation as a counterpart operation of said second conversion processof converting said second information-bit sequence, a decoding operationis performed to produce said second information-bit sequence on thebasis of information on said first encoded sequence and on the basis ofsaid received value; and said first decoding process of carrying out adecoding operation as a counterpart operation of said first conversionprocess of converting said first information-bit sequence, a decodingoperation is performed to produce said first information-bit sequence onthe basis of information on said second encoded sequence obtained as aresult of said decoding operation carried out by said second decodingprocess and on the basis of said received value.
 51. An informationreception method according to claim 48, wherein said first decodingprocess of carrying out a decoding operation as a counterpart operationof said first conversion process of converting said firstinformation-bit sequence and said second decoding process of carryingout a decoding operation as a counterpart operation of said secondconversion process of converting said second information-bit sequenceeach include a likelihood computation process of computing a likelihoodregarding a reception symbol from said received value.
 52. Aninformation reception method according to claim 51, wherein: on thebasis of priori probability information for an encoded sequence otherthan said first encoded sequence and on the basis of said receivedvalue, in said first decoding process of carrying out a decodingoperation as a counterpart operation of said first conversion process ofconverting said first information-bit sequence, posteriori probabilityinformation for said first information-bit sequence is found and outputas a result of said decoding operation, and posteriori probabilityinformation for said first encoded sequence is found and output; and onthe basis of priori probability information for an encoded sequenceother than said second encoded sequence and on the basis of saidreceived value, in said second decoding process of carrying out adecoding operation as a counterpart operation of said second conversionprocess of converting said second information-bit sequence, posterioriprobability information for said second information-bit sequence isfound and output as a result of said decoding operation, and posterioriprobability information for said second encoded sequence is found andoutput.
 53. An information reception method according to claim 52,wherein: on the basis of priori probability information for said firstencoded sequence and on the basis of said received value, in said seconddecoding process of carrying out a decoding operation as a counterpartoperation of said second conversion process of converting said secondinformation-bit sequence, posteriori probability information for saidsecond information-bit sequence is found and output as a result of saiddecoding operation, and posteriori probability information for saidsecond encoded sequence is found and output as priori probabilityinformation for said second encoded sequence to said first decodingprocess of carrying out a decoding operation as a counterpart operationof said first conversion process of converting said firstinformation-bit sequence; and on the basis of priori probabilityinformation for said second encoded sequence received from said seconddecoding process of carrying out a decoding operation as a counterpartoperation of said second conversion process of converting said secondinformation-bit sequence and on the basis of said received value, insaid first decoding process of carrying out a decoding operation as acounterpart operation of said first conversion process of convertingsaid first information-bit sequence, posteriori probability informationfor said first information-bit sequence is found and output as a resultof said decoding operation, and posteriori probability information forsaid first encoded sequence is found and output as priori probabilityinformation for said first encoded sequence to said second decodingprocess of carrying out a decoding operation as a counterpart operationof said second conversion process of converting said secondinformation-bit sequence.
 54. An information reception method accordingto claim 46, wherein, in said decoding process of carrying out adecoding operation to produce at least a information-bit sequence, a MAPdecoding operation or a decoding operation conforming to said MAPdecoding operation is performed.
 55. An information reception methodaccording to claim 46, wherein, in said decoding process of carrying outa decoding operation to produce at least a information-bit sequence,decoding operations are performed to generate information-bit sequencessequentially starting with a highest-order second information-bitsequence subjected to an addition operation last in said additionprocess of producing said additive encoded sequence.
 56. An informationreception method according to claim 46, wherein said decoding process ofcarrying out a decoding operation to produce at least a information-bitsequence, a zigzag or repetitive decoding operation is performed.
 57. Aninformation reception method according to claim 46, wherein: saiddecoding process of carrying out a decoding operation to produce atleast a information-bit sequence has a likelihood computation process ofcomputing a likelihood regarding a reception symbol from said receivedvalue; and if at least one of said first encoded sequence and saidsecond encoded sequence has been encoded, in said likelihood computationprocess, a constituent that maximizes posteriori probability informationfor any constituent is selected as a best candidate to be used as prioriprobability information for an encoded sequence in an operation to finda likelihood for another encoded sequence.
 58. An information receptionmethod according to claim 46, wherein: said decoding process of carryingout a decoding operation to produce at least a information-bit sequencehas a likelihood computation process of computing a likelihood regardinga reception symbol from said received value; and if at least one of saidfirst encoded sequence and said second encoded sequence has beenencoded, in said likelihood computation process, an expected value forany arbitrary constituent already subjected to a soft decision is foundas posteriori probability information to be used as priori probabilityinformation for an encoded sequence in an operation to find a likelihoodfor another encoded sequence.
 59. An information reception methodaccording to claim 46, wherein: said decoding process of carrying out adecoding operation to produce at least a information-bit sequence has alikelihood computation process of computing a likelihood regarding areception symbol from said received value; and if an encoded sequencenot decoded yet is found to exist in an attempt to decode one of saidfirst encoded sequence and said second encoded sequence, in saidlikelihood computation process, a likelihood for an encoded sequence isfound by regarding said encoded sequence not decoded yet as a Gaussiannoise having an equal electric power.
 60. An information receptionmethod according to claim 46, further comprising: a re-encoding process,which is carried out for re-encoding a highest-order secondinformation-bit sequence by using posteriori probability information forsaid second information-bit sequence upon completion of a decodingoperation performed in said decoding process of carrying out a decodingoperation to produce at least a information-bit sequence, that is, uponcompletion of a decoding operation to generate said highest-order secondinformation-bit sequence subjected last to an addition operation carriedout in said addition process of producing said additive encodedsequence; a correlation computation process of finding a correlationbetween a hard-decision value sequence and said received value wheresaid a hard-decision value sequence is an estimated value of said secondencoded value obtained as a result of a re-encoding operation carriedout in said re-encoding process of carrying out a re-encoding operation;and a channel estimation process of estimating an amplitude of acommunication line by using a correlation value found in saidcorrelation computation process of finding a correlation between ahard-decision value sequence and said received value.
 61. An informationreception method according to claim 46, further comprising: are-encoding process, which is carried out for re-encoding ahighest-order second information-bit sequence by using posterioriprobability information for said second encoded sequence upon completionof a decoding operation performed in said decoding process of carryingout a decoding operation to produce at least a information-bit sequence,that is, upon completion of a decoding operation to generate saidhighest-order second information-bit sequence subjected last to anaddition operation carried out in said addition process of producingsaid additive encoded sequence; a correlation computation process offinding a correlation between a hard-decision value sequence and saidreceived value where said a hard-decision value sequence is an estimatedvalue of said second encoded value obtained as a result of a re-encodingoperation carried out in said re-encoding process of carrying out are-encoding operation; and a channel estimation process of estimating anamplitude of a communication line by using a correlation value found insaid correlation computation process of finding a correlation between ahard-decision value sequence and said received value.
 62. An informationreception method according to claim 46, wherein: there is furtherprovided a discrimination process of discriminating a state of acommunication line; and said first and second constants are determinedon the basis of a state of said communication line discriminated in saiddiscrimination process of discriminating a state of said communicationline.
 63. An information reception method according to claim 46, whereinsaid reception process of receiving said reception signal, said firstand second constants determined in accordance with said informationtransmission method on the basis of a state of a communication linediscriminated in accordance with said information transmission methodare received.
 64. An information transmission method according to claim63, wherein: said determined first and second constants are multiplexedin a highest-order second information-bit sequence subjected last to anaddition operation carried out in said addition process of producingsaid additive encoded sequence; and there is further provided aseparation process of separating said first and second constants fromsaid second information-bit sequence.
 65. An information receptionmethod according to claim 46, wherein: when said first encoded sequenceis regarded as a sequence to be transmitted through a communication linealong which a noise is added, in said first multiplication process ofmultiplying said first encoded sequence by said first constant, saidfirst encoded sequence is multiplied by said first constant set so as tosufficiently reduce a bit error rate for said first information-bitsequence; and when said second encoded sequence is regarded as asequence to be transmitted through a communication line along which asum of said noise and a sequence having the same statisticalcharacteristic as said first constant-times encoded sequence is added,in said second multiplication process of multiplying said second encodedsequence by said second constant, said second encoded sequence ismultiplied by said second constant set so as to sufficiently reduce abit error rate for said second information-bit sequence.
 66. Aninformation reception method according to claim 46, wherein: when saidfirst encoded sequence is regarded as a sequence to be transmittedthrough a communication line along which a noise is added, in said firstmultiplication process of multiplying said first encoded sequence bysaid first constant, said first encoded sequence is multiplied by saidfirst constant set so as to sufficiently reduce a bit error rate forsaid first information-bit sequence; and when said second encodedsequence is regarded as a sequence to be transmitted through acommunication line along which a sum of a noise greater in magnitudethan said noise by a predetermined amount and a sequence having the samestatistical characteristic as said first constant-times encoded sequenceis added, in said second multiplication process of multiplying saidsecond encoded sequence by said second constant, said second encodedsequence is multiplied by said second constant set so as to sufficientlyreduce a bit error rate for said second information-bit sequence.